Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities

Jing Zhang; Shujie Li; Yuwen Wang; Xiaoping Xue

doi:10.1016/j.jmaa.2010.05.045

Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities

Jing Zhang^*
, Shujie Li
, Yuwen Wang
, Xiaoping Xue

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology
Yuan-Yung Tseng Functional Analysis Research Center
CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We obtain nonconstant solutions of semilinear elliptic Neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type (I_l), l > 2 and (II_l), l ≥ 1 regions formed by the curves of the Fucik spectrum. Furthermore, we have at least two nonconstant solutions in every order interval under resonance case. In this paper, we apply the sub-sup solution method, Fucik spectrum, mountain pass theorem in order intervals, degree theory and Morse theory to get the conclusions.

Original language	English
Pages (from-to)	682-690
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	371
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2010.05.045
State	Published - Nov 2010

Keywords

Degree theory
Fucik spectrum
Jumping nonlinearity
Morse theory
Multiple solutions
Neumann boundary condition
Semilinear elliptic equations

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10.1016/j.jmaa.2010.05.045

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title = "Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities",

abstract = "We obtain nonconstant solutions of semilinear elliptic Neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type (Il), l > 2 and (IIl), l ≥ 1 regions formed by the curves of the Fucik spectrum. Furthermore, we have at least two nonconstant solutions in every order interval under resonance case. In this paper, we apply the sub-sup solution method, Fucik spectrum, mountain pass theorem in order intervals, degree theory and Morse theory to get the conclusions.",

keywords = "Degree theory, Fucik spectrum, Jumping nonlinearity, Morse theory, Multiple solutions, Neumann boundary condition, Semilinear elliptic equations",

author = "Jing Zhang and Shujie Li and Yuwen Wang and Xiaoping Xue",

year = "2010",

month = nov,

doi = "10.1016/j.jmaa.2010.05.045",

language = "英语",

volume = "371",

pages = "682--690",

journal = "Journal of Mathematical Analysis and Applications",

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TY - JOUR

T1 - Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities

AU - Zhang, Jing

AU - Li, Shujie

AU - Wang, Yuwen

AU - Xue, Xiaoping

PY - 2010/11

Y1 - 2010/11

N2 - We obtain nonconstant solutions of semilinear elliptic Neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type (Il), l > 2 and (IIl), l ≥ 1 regions formed by the curves of the Fucik spectrum. Furthermore, we have at least two nonconstant solutions in every order interval under resonance case. In this paper, we apply the sub-sup solution method, Fucik spectrum, mountain pass theorem in order intervals, degree theory and Morse theory to get the conclusions.

AB - We obtain nonconstant solutions of semilinear elliptic Neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type (Il), l > 2 and (IIl), l ≥ 1 regions formed by the curves of the Fucik spectrum. Furthermore, we have at least two nonconstant solutions in every order interval under resonance case. In this paper, we apply the sub-sup solution method, Fucik spectrum, mountain pass theorem in order intervals, degree theory and Morse theory to get the conclusions.

KW - Degree theory

KW - Fucik spectrum

KW - Jumping nonlinearity

KW - Morse theory

KW - Multiple solutions

KW - Neumann boundary condition

KW - Semilinear elliptic equations

UR - https://www.scopus.com/pages/publications/77955268635

U2 - 10.1016/j.jmaa.2010.05.045

DO - 10.1016/j.jmaa.2010.05.045

M3 - 文章

AN - SCOPUS:77955268635

SN - 0022-247X

VL - 371

SP - 682

EP - 690

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities

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Keywords

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