-
Previous Article
Remarks on nonlinear elastic waves in the radial symmetry in 2-D
- DCDS Home
- This Issue
-
Next Article
Planar quasi-homogeneous polynomial systems with a given weight degree
Principal eigenvalues for some nonlocal eigenvalue problems and applications
1. | School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China, China |
References:
[1] |
F. Andreu-Vaillo, J. M. Mazón, J. D. Rossi and J. Toledo-Melero, Nonlocal Diffusion Problems, Mathematical Surveys and Monographs, AMS, Providence, Rhode Island, 2010.
doi: 10.1090/surv/165. |
[2] |
P. Bates, P. Fife, X. Ren and X. Wang, Travelling waves in a convolution model for phase transitions, Arch. Ration. Mech. Anal., 138 (1997), 105-136.
doi: 10.1007/s002050050037. |
[3] |
P. Bates and A. Chmaj, An integrodifferential model for phase transitions: Stationary solutions in higher space dimensions, J. Statist. Phys., 95 (1999), 1119-1139.
doi: 10.1023/A:1004514803625. |
[4] |
P. Bates and G. Zhao, Existence, uniquenss, and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal, J. Math. Anal. Appl., 332 (2007), 428-440.
doi: 10.1016/j.jmaa.2006.09.007. |
[5] |
H. Berestycki, Le nombre de solutions de certains problèmes semi-linéaires elliptiques, J. Funct. Anal., 40 (1981), 1-29.
doi: 10.1016/0022-1236(81)90069-0. |
[6] |
H. Berestycki, L. Nirenberg and S. R. S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math., 47 (1994), 47-92.
doi: 10.1002/cpa.3160470105. |
[7] |
H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. I. Species persistence, J. Math. Biol., 51 (2005), 75-113.
doi: 10.1007/s00285-004-0313-3. |
[8] |
E. Chasseigne, M. Chaves and J. D. Rossi, Asymptotic behavior for nonlocal diffusion equation, J. Math. Pures Appl., 86 (2006), 271-291.
doi: 10.1016/j.matpur.2006.04.005. |
[9] |
C. Cortazar, M. Elgueta, J. D. Rossi and N. Wolanski, How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems, Arch. Ration. Mech. Anal., 187 (2008), 137-156.
doi: 10.1007/s00205-007-0062-8. |
[10] |
C. Cortázar, M. Elgueta and J. D. Rossi, Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions, Israel J. Math., 170 (2009), 53-60.
doi: 10.1007/s11856-009-0019-8. |
[11] |
J. Coville, J. Dávila and S. Martínez, Existence and uniqueness of solutions to nonlocal equation with monostable nonlinearity, SIAM J. Math. Anal., 39 (2008), 1693-1709.
doi: 10.1137/060676854. |
[12] |
J. Coville, On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators, J. Differential Equations, 249 (2010), 2921-2953.
doi: 10.1016/j.jde.2010.07.003. |
[13] |
J. Coville, J. Dávila and S. Martínez, Pulsating fronts for nonlocal dispersion and KPP nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire, 30 (2013), 179-223.
doi: 10.1016/j.anihpc.2012.07.005. |
[14] |
J. Coville, Nonlocal refuge model with a partial control, Discrete Contin. Dyn. Syst., 35 (2015), 1421-1446.
doi: 10.3934/dcds.2015.35.1421. |
[15] |
R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Ser. Math. Comput. Biol., John Wiley and Sons, Chichester, UK, 2003.
doi: 10.1002/0470871296. |
[16] |
Y. Du and Q. Huang, Blow-up solutions for a class of semilinear elliptic and parabolic equations, SIAM J. Math. Anal., 31 (1999), 1-18.
doi: 10.1137/S0036141099352844. |
[17] |
J. M. Fraile, P. Koch Medina, J. López-Gómez and S. Merino, Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equation, J. Differential Equations, 127 (1996), 295-319.
doi: 10.1006/jdeq.1996.0071. |
[18] |
P. Fife, Some nonclassical trends in parabolic and parabolic-like evolutions, in Trends in Nonlinear Analysis, Springer, Berlin, (2003), 153-191. |
[19] |
J. García-Melián, R. Gómez-Reñasco, J. López-Gómez and J. C. Sabina de Lis, Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs, Arch. Ration. Mech. Anal., 145 (1998), 261-289.
doi: 10.1007/s002050050130. |
[20] |
J. García-Melián and J. D. Rossi, A logistic equation with refuge and nonlocal diffusion, Commun. Pure Appl. Anal., 8 (2009), 2037-2053.
doi: 10.3934/cpaa.2009.8.2037. |
[21] |
J. García-Melián and J. D. Rossi, On the principal eigenvalue of some nonlocal diffusion problems, J. Differential Equations, 246 (2009), 21-38.
doi: 10.1016/j.jde.2008.04.015. |
[22] |
M. Grinfeld, G. Hines, V. Hutson, K. Mischaikow, G. T. Vickers, Non-local dispersal, Differential Integral Equations, 18 (2005), 1299-1320. |
[23] |
V. Hutson, S. Martinez, K. Mischaikow and G. T. Vickers, The evolution of dispersal, J. Math. Biol., 47 (2003), 483-517.
doi: 10.1007/s00285-003-0210-1. |
[24] |
L. I. Ignat and J. D. Rossi, Decay estimates for nonlocal problems via energy methods, J. Math. Pures Appl., 92 (2009), 163-187.
doi: 10.1016/j.matpur.2009.04.009. |
[25] |
Y. Jin and M. A. Lewis, Seasonal influences on population spread and persistence in streams: Critical domain size, SIAM J. Appl. Math., 71 (2011), 1241-1262.
doi: 10.1137/100788033. |
[26] |
Y. Jin and M. A. Lewis, Seasonal influences on population spread and persistence in streams: Spreading speeds, J. Math. Biol., 65 (2012), 403-439.
doi: 10.1007/s00285-011-0465-x. |
[27] |
C. Y. Kao, Y. Lou and W. Shen, Random dispersal vs non-local dispersal, Discrete Contin. Dyn. Syst., 26 (2010), 551-596.
doi: 10.3934/dcds.2010.26.551. |
[28] |
W. T. Li, Y. J. Sun and Z. C. Wang, Entire solutions in the Fisher-KPP equation with nonlocal dispersal, Nonlinear Anal. Real World Appl., 11 (2010), 2302-2313.
doi: 10.1016/j.nonrwa.2009.07.005. |
[29] |
J. López-Gómez, The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems, J. Differential Equations, 127 (1996), 263-294.
doi: 10.1006/jdeq.1996.0070. |
[30] |
J. López-Gómez and J. C. Sabina de Lis, First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs, J. Differential Equations, 148 (1998), 47-64.
doi: 10.1006/jdeq.1998.3456. |
[31] |
T. Ouyang, On the positive solutions of semilinear equations $\Delta u+\lambda u-hu^p=0$, Trans. Amer. Math. Soc., 331 (1992), 503-527.
doi: 10.2307/2154124. |
[32] |
S. Pan, W. T. Li and G. Lin, Travelling wave fronts in nonlocal reaction-diffusion systems and applications, Z. Angew. Math. Phys., 60 (2009), 377-392.
doi: 10.1007/s00033-007-7005-y. |
[33] |
J. W. Sun, W. T. Li and F. Y. Yang, Approximate the Fokker-Planck equation by a class of nonlocal dispersal problems, Nonlinear Anal., 74 (2011), 3501-3509.
doi: 10.1016/j.na.2011.02.034. |
[34] |
J. W. Sun, F. Y. Yang and W. T. Li, A nonlocal dispersal equation arising from a selection-migration model in genetics, J. Differential Equations, 257 (2014), 1372-1402.
doi: 10.1016/j.jde.2014.05.005. |
[35] |
J. W. Sun, W. T. Li and Z. C. Wang, A nonlocal dispersal logistic model with spatial degeneracy, Discrete Contin. Dyn. Syst., 35 (2015), 3217-3238.
doi: 10.3934/dcds.2015.35.3217. |
[36] |
Y. J. Sun, W. T. Li and Z. C. Wang, Entire solutions in nonlocal dispersal equations with bistable nonlinearity, J. Differential Equations, 251 (2011), 551-581.
doi: 10.1016/j.jde.2011.04.020. |
[37] |
Y. J. Sun, W. T. Li and Z. C. Wang, Traveling waves for a nonlocal anisotropic dispersal equation with monostable nonlinearity, Nonlinear Anal., 74 (2011), 814-826.
doi: 10.1016/j.na.2010.09.032. |
[38] |
W. Shen and A. Zhang, Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats, J. Differential Equations, 249 (2010), 747-795.
doi: 10.1016/j.jde.2010.04.012. |
[39] |
W. Shen and A. Zhang, Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats, Proc. Amer. Math. Soc., 140 (2012), 1681-1696.
doi: 10.1090/S0002-9939-2011-11011-6. |
[40] |
J. G. Skellam, Random dispersal in theoretical populations, Biometrika, 38 (1951), 196-218.
doi: 10.1093/biomet/38.1-2.196. |
[41] |
G. B. Zhang, W. T. Li and Y. J. Sun, Asymptotic behavior for nonlocal dispersal equations, Nonlinear Anal., 72 (2010), 4466-4474.
doi: 10.1016/j.na.2010.02.021. |
show all references
References:
[1] |
F. Andreu-Vaillo, J. M. Mazón, J. D. Rossi and J. Toledo-Melero, Nonlocal Diffusion Problems, Mathematical Surveys and Monographs, AMS, Providence, Rhode Island, 2010.
doi: 10.1090/surv/165. |
[2] |
P. Bates, P. Fife, X. Ren and X. Wang, Travelling waves in a convolution model for phase transitions, Arch. Ration. Mech. Anal., 138 (1997), 105-136.
doi: 10.1007/s002050050037. |
[3] |
P. Bates and A. Chmaj, An integrodifferential model for phase transitions: Stationary solutions in higher space dimensions, J. Statist. Phys., 95 (1999), 1119-1139.
doi: 10.1023/A:1004514803625. |
[4] |
P. Bates and G. Zhao, Existence, uniquenss, and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal, J. Math. Anal. Appl., 332 (2007), 428-440.
doi: 10.1016/j.jmaa.2006.09.007. |
[5] |
H. Berestycki, Le nombre de solutions de certains problèmes semi-linéaires elliptiques, J. Funct. Anal., 40 (1981), 1-29.
doi: 10.1016/0022-1236(81)90069-0. |
[6] |
H. Berestycki, L. Nirenberg and S. R. S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math., 47 (1994), 47-92.
doi: 10.1002/cpa.3160470105. |
[7] |
H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. I. Species persistence, J. Math. Biol., 51 (2005), 75-113.
doi: 10.1007/s00285-004-0313-3. |
[8] |
E. Chasseigne, M. Chaves and J. D. Rossi, Asymptotic behavior for nonlocal diffusion equation, J. Math. Pures Appl., 86 (2006), 271-291.
doi: 10.1016/j.matpur.2006.04.005. |
[9] |
C. Cortazar, M. Elgueta, J. D. Rossi and N. Wolanski, How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems, Arch. Ration. Mech. Anal., 187 (2008), 137-156.
doi: 10.1007/s00205-007-0062-8. |
[10] |
C. Cortázar, M. Elgueta and J. D. Rossi, Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions, Israel J. Math., 170 (2009), 53-60.
doi: 10.1007/s11856-009-0019-8. |
[11] |
J. Coville, J. Dávila and S. Martínez, Existence and uniqueness of solutions to nonlocal equation with monostable nonlinearity, SIAM J. Math. Anal., 39 (2008), 1693-1709.
doi: 10.1137/060676854. |
[12] |
J. Coville, On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators, J. Differential Equations, 249 (2010), 2921-2953.
doi: 10.1016/j.jde.2010.07.003. |
[13] |
J. Coville, J. Dávila and S. Martínez, Pulsating fronts for nonlocal dispersion and KPP nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire, 30 (2013), 179-223.
doi: 10.1016/j.anihpc.2012.07.005. |
[14] |
J. Coville, Nonlocal refuge model with a partial control, Discrete Contin. Dyn. Syst., 35 (2015), 1421-1446.
doi: 10.3934/dcds.2015.35.1421. |
[15] |
R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Ser. Math. Comput. Biol., John Wiley and Sons, Chichester, UK, 2003.
doi: 10.1002/0470871296. |
[16] |
Y. Du and Q. Huang, Blow-up solutions for a class of semilinear elliptic and parabolic equations, SIAM J. Math. Anal., 31 (1999), 1-18.
doi: 10.1137/S0036141099352844. |
[17] |
J. M. Fraile, P. Koch Medina, J. López-Gómez and S. Merino, Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equation, J. Differential Equations, 127 (1996), 295-319.
doi: 10.1006/jdeq.1996.0071. |
[18] |
P. Fife, Some nonclassical trends in parabolic and parabolic-like evolutions, in Trends in Nonlinear Analysis, Springer, Berlin, (2003), 153-191. |
[19] |
J. García-Melián, R. Gómez-Reñasco, J. López-Gómez and J. C. Sabina de Lis, Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs, Arch. Ration. Mech. Anal., 145 (1998), 261-289.
doi: 10.1007/s002050050130. |
[20] |
J. García-Melián and J. D. Rossi, A logistic equation with refuge and nonlocal diffusion, Commun. Pure Appl. Anal., 8 (2009), 2037-2053.
doi: 10.3934/cpaa.2009.8.2037. |
[21] |
J. García-Melián and J. D. Rossi, On the principal eigenvalue of some nonlocal diffusion problems, J. Differential Equations, 246 (2009), 21-38.
doi: 10.1016/j.jde.2008.04.015. |
[22] |
M. Grinfeld, G. Hines, V. Hutson, K. Mischaikow, G. T. Vickers, Non-local dispersal, Differential Integral Equations, 18 (2005), 1299-1320. |
[23] |
V. Hutson, S. Martinez, K. Mischaikow and G. T. Vickers, The evolution of dispersal, J. Math. Biol., 47 (2003), 483-517.
doi: 10.1007/s00285-003-0210-1. |
[24] |
L. I. Ignat and J. D. Rossi, Decay estimates for nonlocal problems via energy methods, J. Math. Pures Appl., 92 (2009), 163-187.
doi: 10.1016/j.matpur.2009.04.009. |
[25] |
Y. Jin and M. A. Lewis, Seasonal influences on population spread and persistence in streams: Critical domain size, SIAM J. Appl. Math., 71 (2011), 1241-1262.
doi: 10.1137/100788033. |
[26] |
Y. Jin and M. A. Lewis, Seasonal influences on population spread and persistence in streams: Spreading speeds, J. Math. Biol., 65 (2012), 403-439.
doi: 10.1007/s00285-011-0465-x. |
[27] |
C. Y. Kao, Y. Lou and W. Shen, Random dispersal vs non-local dispersal, Discrete Contin. Dyn. Syst., 26 (2010), 551-596.
doi: 10.3934/dcds.2010.26.551. |
[28] |
W. T. Li, Y. J. Sun and Z. C. Wang, Entire solutions in the Fisher-KPP equation with nonlocal dispersal, Nonlinear Anal. Real World Appl., 11 (2010), 2302-2313.
doi: 10.1016/j.nonrwa.2009.07.005. |
[29] |
J. López-Gómez, The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems, J. Differential Equations, 127 (1996), 263-294.
doi: 10.1006/jdeq.1996.0070. |
[30] |
J. López-Gómez and J. C. Sabina de Lis, First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs, J. Differential Equations, 148 (1998), 47-64.
doi: 10.1006/jdeq.1998.3456. |
[31] |
T. Ouyang, On the positive solutions of semilinear equations $\Delta u+\lambda u-hu^p=0$, Trans. Amer. Math. Soc., 331 (1992), 503-527.
doi: 10.2307/2154124. |
[32] |
S. Pan, W. T. Li and G. Lin, Travelling wave fronts in nonlocal reaction-diffusion systems and applications, Z. Angew. Math. Phys., 60 (2009), 377-392.
doi: 10.1007/s00033-007-7005-y. |
[33] |
J. W. Sun, W. T. Li and F. Y. Yang, Approximate the Fokker-Planck equation by a class of nonlocal dispersal problems, Nonlinear Anal., 74 (2011), 3501-3509.
doi: 10.1016/j.na.2011.02.034. |
[34] |
J. W. Sun, F. Y. Yang and W. T. Li, A nonlocal dispersal equation arising from a selection-migration model in genetics, J. Differential Equations, 257 (2014), 1372-1402.
doi: 10.1016/j.jde.2014.05.005. |
[35] |
J. W. Sun, W. T. Li and Z. C. Wang, A nonlocal dispersal logistic model with spatial degeneracy, Discrete Contin. Dyn. Syst., 35 (2015), 3217-3238.
doi: 10.3934/dcds.2015.35.3217. |
[36] |
Y. J. Sun, W. T. Li and Z. C. Wang, Entire solutions in nonlocal dispersal equations with bistable nonlinearity, J. Differential Equations, 251 (2011), 551-581.
doi: 10.1016/j.jde.2011.04.020. |
[37] |
Y. J. Sun, W. T. Li and Z. C. Wang, Traveling waves for a nonlocal anisotropic dispersal equation with monostable nonlinearity, Nonlinear Anal., 74 (2011), 814-826.
doi: 10.1016/j.na.2010.09.032. |
[38] |
W. Shen and A. Zhang, Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats, J. Differential Equations, 249 (2010), 747-795.
doi: 10.1016/j.jde.2010.04.012. |
[39] |
W. Shen and A. Zhang, Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats, Proc. Amer. Math. Soc., 140 (2012), 1681-1696.
doi: 10.1090/S0002-9939-2011-11011-6. |
[40] |
J. G. Skellam, Random dispersal in theoretical populations, Biometrika, 38 (1951), 196-218.
doi: 10.1093/biomet/38.1-2.196. |
[41] |
G. B. Zhang, W. T. Li and Y. J. Sun, Asymptotic behavior for nonlocal dispersal equations, Nonlinear Anal., 72 (2010), 4466-4474.
doi: 10.1016/j.na.2010.02.021. |
[1] |
Julián Fernández Bonder, Analía Silva, Juan F. Spedaletti. Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2125-2140. doi: 10.3934/dcds.2020355 |
[2] |
Telma Silva, Adélia Sequeira, Rafael F. Santos, Jorge Tiago. Existence, uniqueness, stability and asymptotic behavior of solutions for a mathematical model of atherosclerosis. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 343-362. doi: 10.3934/dcdss.2016.9.343 |
[3] |
Wenxian Shen, Xiaoxia Xie. On principal spectrum points/principal eigenvalues of nonlocal dispersal operators and applications. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1665-1696. doi: 10.3934/dcds.2015.35.1665 |
[4] |
J. Húska, Peter Poláčik, M.V. Safonov. Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Conference Publications, 2005, 2005 (Special) : 427-435. doi: 10.3934/proc.2005.2005.427 |
[5] |
Tomás Caraballo, Xiaoying Han. A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1079-1101. doi: 10.3934/dcdss.2015.8.1079 |
[6] |
J. R. L. Webb. Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 177-186. doi: 10.3934/dcdss.2008.1.177 |
[7] |
Zongming Guo, Xiaohong Guan, Yonggang Zhao. Uniqueness and asymptotic behavior of solutions of a biharmonic equation with supercritical exponent. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 2613-2636. doi: 10.3934/dcds.2019109 |
[8] |
Gabriele Bonanno, Pasquale Candito, Roberto Livrea, Nikolaos S. Papageorgiou. Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1169-1188. doi: 10.3934/cpaa.2017057 |
[9] |
Luiz F. O. Faria. Existence and uniqueness of positive solutions for singular biharmonic elliptic systems. Conference Publications, 2015, 2015 (special) : 400-408. doi: 10.3934/proc.2015.0400 |
[10] |
Shinji Adachi, Masataka Shibata, Tatsuya Watanabe. Asymptotic behavior of positive solutions for a class of quasilinear elliptic equations with general nonlinearities. Communications on Pure and Applied Analysis, 2014, 13 (1) : 97-118. doi: 10.3934/cpaa.2014.13.97 |
[11] |
Yinbin Deng, Qi Gao. Asymptotic behavior of the positive solutions for an elliptic equation with Hardy term. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 367-380. doi: 10.3934/dcds.2009.24.367 |
[12] |
Kun Li, Jianhua Huang, Xiong Li. Asymptotic behavior and uniqueness of traveling wave fronts in a delayed nonlocal dispersal competitive system. Communications on Pure and Applied Analysis, 2017, 16 (1) : 131-150. doi: 10.3934/cpaa.2017006 |
[13] |
Lingju Kong, Roger Nichols. On principal eigenvalues of biharmonic systems. Communications on Pure and Applied Analysis, 2021, 20 (1) : 1-15. doi: 10.3934/cpaa.2020254 |
[14] |
Giovany M. Figueiredo, Tarcyana S. Figueiredo-Sousa, Cristian Morales-Rodrigo, Antonio Suárez. Existence of positive solutions of an elliptic equation with local and nonlocal variable diffusion coefficient. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3689-3711. doi: 10.3934/dcdsb.2018311 |
[15] |
G. Deugoué, T. Tachim Medjo. The Stochastic 3D globally modified Navier-Stokes equations: Existence, uniqueness and asymptotic behavior. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2593-2621. doi: 10.3934/cpaa.2018123 |
[16] |
Yichen Zhang, Meiqiang Feng. A coupled $ p $-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 1419-1438. doi: 10.3934/era.2020075 |
[17] |
Kosuke Ono. Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 651-662. doi: 10.3934/dcds.2003.9.651 |
[18] |
Haitao Yang. On the existence and asymptotic behavior of large solutions for a semilinear elliptic problem in $R^n$. Communications on Pure and Applied Analysis, 2005, 4 (1) : 187-198. doi: 10.3934/cpaa.2005.4.197 |
[19] |
Thi Tuyen Nguyen. Large time behavior of solutions of local and nonlocal nondegenerate Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator. Communications on Pure and Applied Analysis, 2019, 18 (3) : 999-1021. doi: 10.3934/cpaa.2019049 |
[20] |
Yongxiu Shi, Haitao Wan. Refined asymptotic behavior and uniqueness of large solutions to a quasilinear elliptic equation in a borderline case. Electronic Research Archive, 2021, 29 (3) : 2359-2373. doi: 10.3934/era.2020119 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]