Multiplicity of Radially Symmetric Small Energy Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators

Mathematics

Yun-Ho Kim¹  JunIk Lee¹ 

[1] Department of Mathematics Education, Sangmyung University, Seoul 03016, Korea;

关键词: radial solution;    quasilinear elliptic equations;    de giorgi iteration;    modified functional methods;    dual fountain theorem;   

DOI  :  10.3390/math8010128

来源: DOAJ

【 摘 要 】

We investigate the multiplicity of radially symmetric solutions for the quasilinear elliptic equation of Kirchhoff type. This paper is devoted to the study of the $L^{\infty }$ -bound of solutions to the problem above by applying De Giorgi’s iteration method and the localization method. Employing this, we provide the existence of multiple small energy radially symmetric solutions whose $L^{\infty }$ -norms converge to zero. We utilize the modified functional method and the dual fountain theorem as the main tools.

【 授权许可】

Unknown