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Infinitely many solutions for a class of modified nonlinear fourth-order elliptic equations on Rn

Guofeng Che|Haibo Chen
대한수학회 (The Korean Mathematical Society)|2017.05|대한수학회보 (Bulletin of the KMS)|제54권 제3호|pp. 895-909

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참고문헌

키워드

genus theorysublinearfourth-order elliptic equationsnontrivial solutions
주제분류수학

초록

This paper is concerned with the following fourth-order elliptic equations $$ \triangle^{2}u-\Delta u+V(x)u-\frac{\kappa}{2}\Delta(u^{2})u=f(x,u),\rm \mbox{ \ \ }in~\mathbb{R}^{N}, $$ where $N\leq6$, $\kappa\geq0$. Under some appropriate assumptions on $V(x)$ and $f(x, u)$, we prove the existence of infinitely many negative-energy solutions for the above system via the genus properties in critical point theory. Some recent results from the literature are extended.

Abstract

This paper is concerned with the following fourth-order elliptic equations $$ \triangle^{2}u-\Delta u+V(x)u-\frac{\kappa}{2}\Delta(u^{2})u=f(x,u),\rm \mbox{ \ \ }in~\mathbb{R}^{N}, $$ where $N\leq6$, $\kappa\geq0$. Under some appropriate assumptions on $V(x)$ and $f(x, u)$, we prove the existence of infinitely many negative-energy solutions for the above system via the genus properties in critical point theory. Some recent results from the literature are extended.

참고문헌 (24)

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