Multiple positive solutions to a class of modified nonlinear Schrodinger equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:415

Article

Chen, Jianqing

关键词: Variational methods;    Modified nonlinear Schrodinger equation;    Sign changing nonlinearity;    Multiple positive solutions;   

DOI  :  10.1016/j.jmaa.2014.01.067

来源: Elsevier

【 摘 要 】

This paper is concerned with the existence and multiplicity of positive solutions of the following equation -u '' + u - 2((vertical bar u vertical bar(2)''))u = a(x)vertical bar u vertical bar(p-2)u + lambda k(x)u where u is an element of H-1(R). We will prove that the modified term 2((vertical bar u vertical bar(2))'')u is helpful to find multiple positive solutions in the case of the nonlinearity with sign changing coefficient a(x). Surprisingly, we do not need a sign condition integral(N)(R) a(x)e(1)(p) dx < 0, which has been proven to be a necessary condition to the existence of positive solutions for semilinear elliptic equations with sign changing nonlinearity (Alama and Tarantello (1993) [1]). (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free