一类渐近线性双调和方程变号解的存在性

The Existence of Variable Number Solutions in a Kind of Asymptotic Biharmonic Equation

本文研究了一类非线性双调和方程变号解的存在性,其非线性项在原点以及在无穷远处都具有渐近线性。通过运用变分方法,证明了该方程有三个非平凡解,其中一个为正解,一个为负解,另一个为变号解。

This paper studies a biharmonic equations whose nonlinear term is asymptotically linear at both zero and infinity. An existence results of sign-changing solution as well as positive and negative solutions is obtained via variational methods.