
Previous Article
Wellposedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data
 CPAA Home
 This Issue

Next Article
Global existence of strong solutions for $2$dimensional NavierStokes equations on exterior domains with growing data at infinity
Two sequences of solutions for indefinite superlinearsublinear elliptic equations with nonlinear boundary conditions
1.  Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 8408502, Japan 
2.  Department of Mathematics, Graduate School of Science, Osaka City University, 33138 Sugimoto Sumiyoshiku, Osakashi, Osaka, 5588585, Japan 
References:
[1] 
A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications,, \emph{J. Funct. Anal.}, 14 (1973), 349. Google Scholar 
[2] 
A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems,, \emph{J. Funct. Anal.}, 122 (1994), 519. doi: 10.1006/jfan.1994.1078. Google Scholar 
[3] 
T. Bartsch and M. Willem, On an elliptic equation with concave and convex nonlinearities,, \emph{Proc. Amer. Math. Soc.}, 123 (1995), 3555. doi: 10.2307/2161107. Google Scholar 
[4] 
D. C. Clark, A variant of the LusternikSchnirelman theory,, \emph{Indiana Univ. Math. J.}, 22 (1972), 65. Google Scholar 
[5] 
D. G. DeFigueiredo, J.P. Gossez and P. Ubilla, Local superlinearity and sublinearity for indefinite semilinear elliptic problems,, \emph{J. Funct. Anal.}, 199 (2003), 452. doi: 10.1016/S00221236(02)000605. Google Scholar 
[6] 
D. G. DeFigueiredo, J.P. Gossez and P. Ubilla, Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity,, \emph{J. Eur. Math. Soc.}, 8 (2006), 269. doi: 10.4171/JEMS/52. Google Scholar 
[7] 
J. GarciaAzorero, I. Peral and J. D. Rossi, A convexconcave problem with a nonlinear boundary condition,, \emph{J. Differential Equations}, 198 (2004), 91. doi: 10.1016/S00220396(03)000688. Google Scholar 
[8] 
R. Kajikiya, A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations,, \emph{J. Funct. Anal.}, 225 (2005), 352. doi: 10.1016/j.jfa.2005.04.005. Google Scholar 
[9] 
R. Kajikiya, Superlinear elliptic equations with singular coefficients on the boundary,, \emph{Nonlinear Analysis, 73 (2010), 2117. doi: 10.1016/j.na.2010.05.039. Google Scholar 
[10] 
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations,, translated by Scripta Technica, (1968). Google Scholar 
[11] 
D. Naimen, Existence of infinitely many solutions for nonlinear Neumann problems with indefinite coefficients,, Submitted for publications., (). Google Scholar 
[12] 
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations,, CBMS Regional Conference Series in Mathematics Vol. 65, (1986). Google Scholar 
[13] 
M. Struwe, Variational Methods,, 2$^{nd}$ edition, (1996). Google Scholar 
[14] 
Z.Q. Wang, Nonlinear boundary value problems with concave nonlinearities near the origin,, \emph{Nonlinear Differential Equations Appl.}, 8 (2001), 15. doi: 10.1007/PL00001436. Google Scholar 
show all references
References:
[1] 
A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications,, \emph{J. Funct. Anal.}, 14 (1973), 349. Google Scholar 
[2] 
A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems,, \emph{J. Funct. Anal.}, 122 (1994), 519. doi: 10.1006/jfan.1994.1078. Google Scholar 
[3] 
T. Bartsch and M. Willem, On an elliptic equation with concave and convex nonlinearities,, \emph{Proc. Amer. Math. Soc.}, 123 (1995), 3555. doi: 10.2307/2161107. Google Scholar 
[4] 
D. C. Clark, A variant of the LusternikSchnirelman theory,, \emph{Indiana Univ. Math. J.}, 22 (1972), 65. Google Scholar 
[5] 
D. G. DeFigueiredo, J.P. Gossez and P. Ubilla, Local superlinearity and sublinearity for indefinite semilinear elliptic problems,, \emph{J. Funct. Anal.}, 199 (2003), 452. doi: 10.1016/S00221236(02)000605. Google Scholar 
[6] 
D. G. DeFigueiredo, J.P. Gossez and P. Ubilla, Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity,, \emph{J. Eur. Math. Soc.}, 8 (2006), 269. doi: 10.4171/JEMS/52. Google Scholar 
[7] 
J. GarciaAzorero, I. Peral and J. D. Rossi, A convexconcave problem with a nonlinear boundary condition,, \emph{J. Differential Equations}, 198 (2004), 91. doi: 10.1016/S00220396(03)000688. Google Scholar 
[8] 
R. Kajikiya, A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations,, \emph{J. Funct. Anal.}, 225 (2005), 352. doi: 10.1016/j.jfa.2005.04.005. Google Scholar 
[9] 
R. Kajikiya, Superlinear elliptic equations with singular coefficients on the boundary,, \emph{Nonlinear Analysis, 73 (2010), 2117. doi: 10.1016/j.na.2010.05.039. Google Scholar 
[10] 
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations,, translated by Scripta Technica, (1968). Google Scholar 
[11] 
D. Naimen, Existence of infinitely many solutions for nonlinear Neumann problems with indefinite coefficients,, Submitted for publications., (). Google Scholar 
[12] 
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations,, CBMS Regional Conference Series in Mathematics Vol. 65, (1986). Google Scholar 
[13] 
M. Struwe, Variational Methods,, 2$^{nd}$ edition, (1996). Google Scholar 
[14] 
Z.Q. Wang, Nonlinear boundary value problems with concave nonlinearities near the origin,, \emph{Nonlinear Differential Equations Appl.}, 8 (2001), 15. doi: 10.1007/PL00001436. Google Scholar 
[1] 
D. Motreanu, Donal O'Regan, Nikolaos S. Papageorgiou. A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems. Communications on Pure & Applied Analysis, 2011, 10 (6) : 17911816. doi: 10.3934/cpaa.2011.10.1791 
[2] 
Liping Wang, Chunyi Zhao. Infinitely many solutions for nonlinear Schrödinger equations with slow decaying of potential. Discrete & Continuous Dynamical Systems  A, 2017, 37 (3) : 17071731. doi: 10.3934/dcds.2017071 
[3] 
Miao Du, Lixin Tian. Infinitely many solutions of the nonlinear fractional Schrödinger equations. Discrete & Continuous Dynamical Systems  B, 2016, 21 (10) : 34073428. doi: 10.3934/dcdsb.2016104 
[4] 
Petru Jebelean. Infinitely many solutions for ordinary $p$Laplacian systems with nonlinear boundary conditions. Communications on Pure & Applied Analysis, 2008, 7 (2) : 267275. doi: 10.3934/cpaa.2008.7.267 
[5] 
Xiying Sun, Qihuai Liu, Dingbian Qian, Na Zhao. Infinitely many subharmonic solutions for nonlinear equations with singular $ \phi $Laplacian. Communications on Pure & Applied Analysis, 2020, 19 (1) : 279292. doi: 10.3934/cpaa.20200015 
[6] 
Lushun Wang, Minbo Yang, Yu Zheng. Infinitely many segregated solutions for coupled nonlinear Schrödinger systems. Discrete & Continuous Dynamical Systems  A, 2019, 39 (10) : 60696102. doi: 10.3934/dcds.2019265 
[7] 
Weiwei Ao, Juncheng Wei, Wen Yang. Infinitely many positive solutions of fractional nonlinear Schrödinger equations with nonsymmetric potentials. Discrete & Continuous Dynamical Systems  A, 2017, 37 (11) : 55615601. doi: 10.3934/dcds.2017242 
[8] 
Weiwei Ao, Liping Wang, Wei Yao. Infinitely many solutions for nonlinear Schrödinger system with nonsymmetric potentials. Communications on Pure & Applied Analysis, 2016, 15 (3) : 965989. doi: 10.3934/cpaa.2016.15.965 
[9] 
Wei Long, Shuangjie Peng, Jing Yang. Infinitely many positive and signchanging solutions for nonlinear fractional scalar field equations. Discrete & Continuous Dynamical Systems  A, 2016, 36 (2) : 917939. doi: 10.3934/dcds.2016.36.917 
[10] 
Weiming Liu, Chunhua Wang. Infinitely many solutions for a nonlinear Schrödinger equation with nonsymmetric electromagnetic fields. Discrete & Continuous Dynamical Systems  A, 2016, 36 (12) : 70817115. doi: 10.3934/dcds.2016109 
[11] 
Rossella Bartolo, Anna Maria Candela, Addolorata Salvatore. Infinitely many solutions for a perturbed Schrödinger equation. Conference Publications, 2015, 2015 (special) : 94102. doi: 10.3934/proc.2015.0094 
[12] 
Andrzej Szulkin, Shoyeb Waliullah. Infinitely many solutions for some singular elliptic problems. Discrete & Continuous Dynamical Systems  A, 2013, 33 (1) : 321333. doi: 10.3934/dcds.2013.33.321 
[13] 
Liang Zhang, X. H. Tang, Yi Chen. Infinitely many solutions for a class of perturbed elliptic equations with nonlocal operators. Communications on Pure & Applied Analysis, 2017, 16 (3) : 823842. doi: 10.3934/cpaa.2017039 
[14] 
Alberto Boscaggin, Anna Capietto. Infinitely many solutions to superquadratic planar Diractype systems. Conference Publications, 2009, 2009 (Special) : 7281. doi: 10.3934/proc.2009.2009.72 
[15] 
Rossella Bartolo, Anna Maria Candela, Addolorata Salvatore. Infinitely many radial solutions of a nonhomogeneous $p$Laplacian problem. Conference Publications, 2013, 2013 (special) : 5159. doi: 10.3934/proc.2013.2013.51 
[16] 
Dušan D. Repovš. Infinitely many symmetric solutions for anisotropic problems driven by nonhomogeneous operators. Discrete & Continuous Dynamical Systems  S, 2019, 12 (2) : 401411. doi: 10.3934/dcdss.2019026 
[17] 
Ziheng Zhang, Rong Yuan. Infinitely many homoclinic solutions for damped vibration problems with subquadratic potentials. Communications on Pure & Applied Analysis, 2014, 13 (2) : 623634. doi: 10.3934/cpaa.2014.13.623 
[18] 
Yinbin Deng, Shuangjie Peng, Li Wang. Infinitely many radial solutions to elliptic systems involving critical exponents. Discrete & Continuous Dynamical Systems  A, 2014, 34 (2) : 461475. doi: 10.3934/dcds.2014.34.461 
[19] 
Philip Korman. Infinitely many solutions and Morse index for nonautonomous elliptic problems. Communications on Pure & Applied Analysis, 2020, 19 (1) : 3146. doi: 10.3934/cpaa.2020003 
[20] 
Liping Wang. Arbitrarily many solutions for an elliptic Neumann problem with sub or supercritical nonlinearity. Communications on Pure & Applied Analysis, 2010, 9 (3) : 761778. doi: 10.3934/cpaa.2010.9.761 
2018 Impact Factor: 0.925
Tools
Metrics
Other articles
by authors
[Back to Top]