Existence and multiplicity results for a semilinear elliptic problem

被引：3

作者：

Castro, Alfonso ^{[1
]}

Cossio, Jorge ^{[2
]}

Herron, Sigifredo ^{[2
]}

Velez, Carlos ^{[2
]}

机构：

[1] Harvey Mudd Coll, Dept Math, Claremont, CA 91711 USA

[2] Univ Nacl Colombia Sede Medellin, Escuela Matemat, Apartado Aereo 3840, Medellin, Colombia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 475卷 / 02期

关键词：

Semilinear elliptic equation; Variational methods; Local degree; A priori estimates; LINEAR DIRICHLET PROBLEM; OPERATOR-EQUATIONS;

D O I：

10.1016/j.jmaa.2019.03.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We make extensive use of variational methods and characterizations of the local degree of critical points. Furthermore, uniqueness and qualitative properties of the solutions are investigated. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：1493 / 1501

页数：9

共 50 条

[31] Existence and multiplicity of positive solutions of semilinear elliptic equations in unbounded domains
Hu, Kai
Tang, Chun-Lei
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (03) : 609 - 629
[32] SHARP MULTIPLICITY RESULTS FOR A SEMILINEAR DIRICHLET PROBLEM
CAC, NP
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (3-4) : 557 - 582
[33] Existence of Entire Solutions of a Singular Semilinear Elliptic Problem
Wei Jie FENG
Xi Yu LIU
[J]. Acta Mathematica Sinica,English Series, 2004, 20 (06) : 983 - 988
[34] Existence of Entire Solutions of a Singular Semilinear Elliptic Problem
Wei Jie Feng
Xi Yu Liu
[J]. Acta Mathematica Sinica, 2004, 20 : 983 - 988
[35] Existence of Entire Solutions of a Singular Semilinear Elliptic Problem
Feng, Wei Jie
Liu, Xi Yu
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2004, 20 (06) : 983 - 988
[36] Multiplicity results for semilinear resonant elliptic problems with discontinuous nonlinearities
Teng, Kaimin
Wu, Man
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (06) : 1652 - 1667
[37] Multiplicity results for semilinear elliptic equations with resonance at higher eigenvalues
Su, JB
Tang, CL
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 44 (03) : 311 - 321
[38] Multiplicity results and qualitative properties for Neumann semilinear elliptic problems
Agudelo, Oscar
Correa, Santiago
Restrepo, Daniel
Velez, Carlos
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 468 (01) : 141 - 160
[39] Multiplicity results for a semilinear, elliptic differential equation with conflicting nonlinearities
Ruppen, HJ
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 147 (01) : 79 - 122
[40] MULTIPLICITY RESULTS FOR SEMILINEAR ELLIPTIC PROBLEMS AT RESONANCE AND WITH JUMPING NONLINEARITIES
HIRANO, N
NISHIMURA, T
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 180 (02) : 566 - 586

← 1 2 3 4 5 →