-
Previous Article
Pentagrams, inscribed polygons, and Prym varieties
- ERA-MS Home
- This Volume
-
Next Article
Asymptotic Hilbert polynomial and a bound for Waldschmidt constants
Nonexistence results for a fully nonlinear evolution inequality
| 1. | School of Science, Hezhou University, Hezhou, 542899, Guangxi Province, China |
References:
| [1] |
L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian, Acta Math., 155 (1985), 261-301.
doi: 10.1007/BF02392544. |
| [2] |
H. Fujita, On the blowing up of solutions of the Cauchy problems for $u_t=\Delta u + u^{1+\alpha}$, J. Fac. Sci. Univ. Tokyo, Sect. I, 13 (1966), 109-124. |
| [3] |
K. Hayakawa, On the nonexistence of global solutions of some semilinear parabolic equations, Proc. Japan Acad., 49 (1973), 503-505.
doi: 10.3792/pja/1195519254. |
| [4] |
D. Labutin, Potential estimates for a class of fully nonlinear elliptic equations, Duke Math. J., 111 (2002), 1-49.
doi: 10.1215/S0012-7094-02-11111-9. |
| [5] |
E. Mitidieri and S. Pohozaev, Towards a unified approach to nonexistence of solutions for a class of differential inequalities, Milan J. Math., 72 (2004), 129-162.
doi: 10.1007/s00032-004-0032-7. |
| [6] |
Q. Ou, Nonexistence results for Hessian inequality, Methods Appl. Anal., 17 (2010), 213-223.
doi: 10.4310/MAA.2010.v17.n2.a5. |
| [7] |
N. C. Phuc and I. E. Verbitsky, Quasilinear and Hessian equations of Lane-Emden type, Ann. of Math., 168 (2008), 859-914.
doi: 10.4007/annals.2008.168.859. |
| [8] |
N. C. Phuc and I. E. Verbitsky, Local integral estimates and removable singularities for quasilinear and Hessian equations with nonlinear source terms, Comm. Partial Differential Equations, 31 (2006), 1779-1791.
doi: 10.1080/03605300600783549. |
| [9] |
N. Trudinger and X.-J. Wang, Hessian measures. I. Dedicated to Olga Ladyzhenskaya, Topo. Methods Nonlinear Anal., 10 (1997), 225-239. |
| [10] |
N. Trudinger and X.-J. Wang, Hessian measures. II, Ann. of Math. (2), 150 (1999), 579-604.
doi: 10.2307/121089. |
| [11] |
N. Trudinger and X.-J. Wang, Hessian measures. III, J. Funct. Anal., 193 (2002), 1-23.
doi: 10.1006/jfan.2001.3925. |
show all references
References:
| [1] |
L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian, Acta Math., 155 (1985), 261-301.
doi: 10.1007/BF02392544. |
| [2] |
H. Fujita, On the blowing up of solutions of the Cauchy problems for $u_t=\Delta u + u^{1+\alpha}$, J. Fac. Sci. Univ. Tokyo, Sect. I, 13 (1966), 109-124. |
| [3] |
K. Hayakawa, On the nonexistence of global solutions of some semilinear parabolic equations, Proc. Japan Acad., 49 (1973), 503-505.
doi: 10.3792/pja/1195519254. |
| [4] |
D. Labutin, Potential estimates for a class of fully nonlinear elliptic equations, Duke Math. J., 111 (2002), 1-49.
doi: 10.1215/S0012-7094-02-11111-9. |
| [5] |
E. Mitidieri and S. Pohozaev, Towards a unified approach to nonexistence of solutions for a class of differential inequalities, Milan J. Math., 72 (2004), 129-162.
doi: 10.1007/s00032-004-0032-7. |
| [6] |
Q. Ou, Nonexistence results for Hessian inequality, Methods Appl. Anal., 17 (2010), 213-223.
doi: 10.4310/MAA.2010.v17.n2.a5. |
| [7] |
N. C. Phuc and I. E. Verbitsky, Quasilinear and Hessian equations of Lane-Emden type, Ann. of Math., 168 (2008), 859-914.
doi: 10.4007/annals.2008.168.859. |
| [8] |
N. C. Phuc and I. E. Verbitsky, Local integral estimates and removable singularities for quasilinear and Hessian equations with nonlinear source terms, Comm. Partial Differential Equations, 31 (2006), 1779-1791.
doi: 10.1080/03605300600783549. |
| [9] |
N. Trudinger and X.-J. Wang, Hessian measures. I. Dedicated to Olga Ladyzhenskaya, Topo. Methods Nonlinear Anal., 10 (1997), 225-239. |
| [10] |
N. Trudinger and X.-J. Wang, Hessian measures. II, Ann. of Math. (2), 150 (1999), 579-604.
doi: 10.2307/121089. |
| [11] |
N. Trudinger and X.-J. Wang, Hessian measures. III, J. Funct. Anal., 193 (2002), 1-23.
doi: 10.1006/jfan.2001.3925. |
| [1] |
William Guo. Streamlining applications of integration by parts in teaching applied calculus. STEM Education, 2022, 2 (1) : 73-83. doi: 10.3934/steme.2022005 |
| [2] |
Xavier Ros-Oton, Joaquim Serra. Local integration by parts and Pohozaev identities for higher order fractional Laplacians. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2131-2150. doi: 10.3934/dcds.2015.35.2131 |
| [3] |
Thabet Abdeljawad. Fractional operators with boundary points dependent kernels and integration by parts. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 351-375. doi: 10.3934/dcdss.2020020 |
| [4] |
Dezhong Chen, Li Ma. A Liouville type Theorem for an integral system. Communications on Pure and Applied Analysis, 2006, 5 (4) : 855-859. doi: 10.3934/cpaa.2006.5.855 |
| [5] |
Pengyan Wang, Pengcheng Niu. Liouville's theorem for a fractional elliptic system. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1545-1558. doi: 10.3934/dcds.2019067 |
| [6] |
Ze Cheng, Genggeng Huang. A Liouville theorem for the subcritical Lane-Emden system. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1359-1377. doi: 10.3934/dcds.2019058 |
| [7] |
Jingbo Dou, Ye Li. Liouville theorem for an integral system on the upper half space. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 155-171. doi: 10.3934/dcds.2015.35.155 |
| [8] |
Xinjing Wang. Liouville type theorem for Fractional Laplacian system. Communications on Pure and Applied Analysis, 2020, 19 (11) : 5253-5268. doi: 10.3934/cpaa.2020236 |
| [9] |
Anh Tuan Duong, Quoc Hung Phan. A Liouville-type theorem for cooperative parabolic systems. Discrete and Continuous Dynamical Systems, 2018, 38 (2) : 823-833. doi: 10.3934/dcds.2018035 |
| [10] |
Xian-gao Liu, Xiaotao Zhang. Liouville theorem for MHD system and its applications. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2329-2350. doi: 10.3934/cpaa.2018111 |
| [11] |
Genggeng Huang. A Liouville theorem of degenerate elliptic equation and its application. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4549-4566. doi: 10.3934/dcds.2013.33.4549 |
| [12] |
Shigeru Sakaguchi. A Liouville-type theorem for some Weingarten hypersurfaces. Discrete and Continuous Dynamical Systems - S, 2011, 4 (4) : 887-895. doi: 10.3934/dcdss.2011.4.887 |
| [13] |
Yuan Li. Extremal solution and Liouville theorem for anisotropic elliptic equations. Communications on Pure and Applied Analysis, 2021, 20 (12) : 4063-4082. doi: 10.3934/cpaa.2021144 |
| [14] |
Xiaohui Yu. Liouville type theorem for nonlinear elliptic equation with general nonlinearity. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4947-4966. doi: 10.3934/dcds.2014.34.4947 |
| [15] |
Xinjing Wang, Pengcheng Niu, Xuewei Cui. A Liouville type theorem to an extension problem relating to the Heisenberg group. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2379-2394. doi: 10.3934/cpaa.2018113 |
| [16] |
Weiwei Zhao, Jinge Yang, Sining Zheng. Liouville type theorem to an integral system in the half-space. Communications on Pure and Applied Analysis, 2014, 13 (2) : 511-525. doi: 10.3934/cpaa.2014.13.511 |
| [17] |
Ovidiu Savin. A Liouville theorem for solutions to the linearized Monge-Ampere equation. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 865-873. doi: 10.3934/dcds.2010.28.865 |
| [18] |
Frank Arthur, Xiaodong Yan, Mingfeng Zhao. A Liouville-type theorem for higher order elliptic systems. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3317-3339. doi: 10.3934/dcds.2014.34.3317 |
| [19] |
Begoña Barrios, Leandro Del Pezzo, Jorge García-Melián, Alexander Quaas. A Liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5731-5746. doi: 10.3934/dcds.2017248 |
| [20] |
Zhenjie Li, Ze Cheng, Dongsheng Li. The Liouville type theorem and local regularity results for nonlinear differential and integral systems. Communications on Pure and Applied Analysis, 2015, 14 (2) : 565-576. doi: 10.3934/cpaa.2015.14.565 |
2020 Impact Factor: 0.929
Tools
Metrics
Other articles
by authors
[Back to Top]