Infinitely many nodal solutions for nonlinear elliptic equations with combined nonlinearities and lack of symmetry

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

He, Tieshan¹  He, Lang² 

[1] Zhongkai Univ Agr & Engn, Sch Computat Sci, Guangzhou 510225, Peoples R China

[2] Sun Yat Sen Univ, Sch Data & Comp Sci, Guangzhou 510006, Peoples R China

关键词: Nodal solutions;    Variational approach;    Gradient flow;    Strong comparison principle;    Concave-convex nonlinearities;   

DOI  :  10.1016/j.jmaa.2020.123889

来源: Elsevier

【 摘 要 】

We present a new approach to studying a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is concave (i.e., (p - 1)-sublinear) near zero and convex (i.e., (p - 1)-superlinear) near +/-infinity. The reaction term is not assumed to be odd. We show that for all small values of the parameter lambda > 0, the problem has infinitely many nodal solutions. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free