Electron. J. Diff. Equ., Vol. 2016 (2016), No. 225, pp. 1-12.

Existence of solutions for Kirchhoff equations with a small perturbations

Yong-Yi Lan

Abstract:
In this article, we consider the Kirchhoff equation
$$\displaylines{ -\Big(a+b\int_{\Omega }|\nabla u|^2dx\Big)\Delta u =f(x,u)+\mu g(x,u),\quad x\in \Omega , \cr u=0,\quad x\in\partial\Omega, }$$
and under suitable assumptions on the main term f in the equation, some existence results are obtained by the variational methods and some analysis techniques.

Submitted February 16, 2016. Published August 18, 2016.
Math Subject Classifications: 35J60, 35J65, 53C35.
Key Words: Kirchhoff equation; Dirichlet boundary condition; mountain pass theorem; perturbation problem.

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Yong-Yi Lan
School of Mathematical Sciences
Xiamen University
Xiamen 361005, China
email: lanyongyi@jmu.edu.cn

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