-
Previous Article
Global existence of strong solutions for $2$-dimensional Navier-Stokes equations on exterior domains with growing data at infinity
- CPAA Home
- This Issue
-
Next Article
Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data
Two sequences of solutions for indefinite superlinear-sublinear elliptic equations with nonlinear boundary conditions
1. | Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502, Japan |
2. | Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto Sumiyoshi-ku, Osaka-shi, Osaka, 558-8585, 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.
|
[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. |
[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. |
[4] |
D. C. Clark, A variant of the Lusternik-Schnirelman theory,, \emph{Indiana Univ. Math. J.}, 22 (1972), 65.
|
[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/S0022-1236(02)00060-5. |
[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. |
[7] |
J. Garcia-Azorero, I. Peral and J. D. Rossi, A convex-concave problem with a nonlinear boundary condition,, \emph{J. Differential Equations}, 198 (2004), 91.
doi: 10.1016/S0022-0396(03)00068-8. |
[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. |
[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. |
[10] |
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations,, translated by Scripta Technica, (1968).
|
[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).
|
[13] |
M. Struwe, Variational Methods,, 2$^{nd}$ edition, (1996).
|
[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. |
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.
|
[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. |
[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. |
[4] |
D. C. Clark, A variant of the Lusternik-Schnirelman theory,, \emph{Indiana Univ. Math. J.}, 22 (1972), 65.
|
[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/S0022-1236(02)00060-5. |
[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. |
[7] |
J. Garcia-Azorero, I. Peral and J. D. Rossi, A convex-concave problem with a nonlinear boundary condition,, \emph{J. Differential Equations}, 198 (2004), 91.
doi: 10.1016/S0022-0396(03)00068-8. |
[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. |
[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. |
[10] |
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations,, translated by Scripta Technica, (1968).
|
[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).
|
[13] |
M. Struwe, Variational Methods,, 2$^{nd}$ edition, (1996).
|
[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. |
[1] |
Sishu Shankar Muni, Robert I. McLachlan, David J. W. Simpson. Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021010 |
[2] |
Ryuji Kajikiya. Existence of nodal solutions for the sublinear Moore-Nehari differential equation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1483-1506. doi: 10.3934/dcds.2020326 |
[3] |
Philippe Laurençot, Christoph Walker. Variational solutions to an evolution model for MEMS with heterogeneous dielectric properties. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 677-694. doi: 10.3934/dcdss.2020360 |
[4] |
Lateef Olakunle Jolaoso, Maggie Aphane. Bregman subgradient extragradient method with monotone self-adjustment stepsize for solving pseudo-monotone variational inequalities and fixed point problems. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020178 |
[5] |
Yuxia Guo, Shaolong Peng. A direct method of moving planes for fully nonlinear nonlocal operators and applications. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020462 |
[6] |
Xiu Ye, Shangyou Zhang, Peng Zhu. A weak Galerkin finite element method for nonlinear conservation laws. Electronic Research Archive, 2021, 29 (1) : 1897-1923. doi: 10.3934/era.2020097 |
[7] |
Ke Su, Yumeng Lin, Chun Xu. A new adaptive method to nonlinear semi-infinite programming. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021012 |
[8] |
Hua Chen, Yawei Wei. Multiple solutions for nonlinear cone degenerate elliptic equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020272 |
[9] |
Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Klein-gordon equation. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020448 |
[10] |
Junyong Eom, Kazuhiro Ishige. Large time behavior of ODE type solutions to nonlinear diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3395-3409. doi: 10.3934/dcds.2019229 |
[11] |
Riadh Chteoui, Abdulrahman F. Aljohani, Anouar Ben Mabrouk. Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system. Electronic Research Archive, , () : -. doi: 10.3934/era.2021002 |
[12] |
Hassan Mohammad. A diagonal PRP-type projection method for convex constrained nonlinear monotone equations. Journal of Industrial & Management Optimization, 2021, 17 (1) : 101-116. doi: 10.3934/jimo.2019101 |
[13] |
Andrew D. Lewis. Erratum for "nonholonomic and constrained variational mechanics". Journal of Geometric Mechanics, 2020, 12 (4) : 671-675. doi: 10.3934/jgm.2020033 |
[14] |
Maoding Zhen, Binlin Zhang, Vicenţiu D. Rădulescu. Normalized solutions for nonlinear coupled fractional systems: Low and high perturbations in the attractive case. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020379 |
[15] |
Zedong Yang, Guotao Wang, Ravi P. Agarwal, Haiyong Xu. Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020436 |
[16] |
Serge Dumont, Olivier Goubet, Youcef Mammeri. Decay of solutions to one dimensional nonlinear Schrödinger equations with white noise dispersion. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020456 |
[17] |
Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276 |
[18] |
Alex H. Ardila, Mykael Cardoso. Blow-up solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (1) : 101-119. doi: 10.3934/cpaa.2020259 |
[19] |
Juhua Shi, Feida Jiang. The degenerate Monge-Ampère equations with the Neumann condition. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020297 |
[20] |
Xing-Bin Pan. Variational and operator methods for Maxwell-Stokes system. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3909-3955. doi: 10.3934/dcds.2020036 |
2019 Impact Factor: 1.105
Tools
Metrics
Other articles
by authors
[Back to Top]