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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:371

Article

Zhang, Jing^1,2  Li, Shujie^2,3  Wang, Yuwen²  Xue, Xiaoping¹ 

[1] Harbin Inst Technol, Dept Math, Harbin, Peoples R China

[2] Yuan Yung Tseng Funct Anal Res Ctr, Harbin 150025, Peoples R China

[3] Acad Sinica, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China

关键词: Semilinear elliptic equations;    Neumann boundary condition;    Multiple solutions;    Jumping nonlinearity;    Fucik spectrum;    Degree theory;    Morse theory;   

DOI  :  10.1016/j.jmaa.2010.05.045

来源: Elsevier

【 摘 要 】

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-t), l > 2 and (IIt), 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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free