Xian Hu, Yong-Yi Lan, Multiple solutions of Kirchhoff equations with a small perturbations, Vol. 2022 (2022), Article ID 19, pp. 1-11

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DOI: 10.23952/jnfa.2022.19

Received March 21, 2022; Accepted April 20, 2022; Published May 14, 2022

 

Abstract In this paper, we consider the following Kirchhoff equation

-\bigg(a+b\int_{\Omega}|\nabla u|^{2}\,\mbox{d}x\bigg)\Delta u = f(x,u)+ tg(x,u),  x\in \Omega,
 u=0,  x\in  \partial \Omega,

with the Dirichlet boundary value. Assuming that the main term f(x,u) is sublinear and odd with respect to u, and the perturbation term is a any continuous function with a small coefficient, we establish the existence and multiplicity of nontrivial solutions for the problem. The approach relies on a combination of variational and minimization methods coupled with the reduction technique.

 

How to Cite this Article:
X. Hu, Y.-Y. Lan, Multiple solutions of Kirchhoff equations with a small perturbations, J. Nonlinear Funct. Anal. 2022 (2022) 19.