Year: 2017
Author: Shiqiang Tang, Peng Chen, Xiaochun Liu
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 2 : pp. 146–164
Abstract
This paper is concerned with the existence of nontrivial solutions for the following fourth-order equations of Kirchhoff type
\begin{equation*}\begin{cases}\Delta^{2}u-\left(a+b\displaystyle\int_{{\mathbb{R}}^N }|\nabla{u}|^2{\rm d}x\right)\Delta{u}+\lambda V(x)u=f(x,u),\quad x\in\mathbb{R}^N ,\\u\in{H^2({\mathbb{R}}^N)},\end{cases}\end{equation*}
where $a,b$ are positive constants, $\lambda \geq 1$ is a parameter, and the nonlinearity $f$ is either superlinear or sublinear at infinity in $u$. With the help of the variational methods, we obtain the existence and multiplicity results in the working spaces.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v30.n2.3
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 2 : pp. 146–164
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Fourth-order elliptic equations