## Taiwanese Journal of Mathematics

### MULTIPLE SOLUTIONS FOR THE NONHOMOGENEOUS FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

#### Abstract

This paper considers the following nonhomogeneous fourth order elliptic equations of Kirchhoff type:\begin{eqnarray*}\begin{cases}\displaystyle\triangle ^2u-(a+b\int_{\text R^N}|\nabla u|^2dx)\triangle u+V(x)u= f(x,u)+h(x),~\text{in}~ \text R^N,\\ \displaystyle u\in H^2(\text R^N), \end{cases}\end{eqnarray*}where constants $a\gt 0,~b\geq0$. Under certain assumptions on $V(x)$, $f(x,u)$ and $h(x)$, we show the existence and multiplicity of solutions  by the Ekeland$^{,}$s variational principle and the Mountain Pass Theorem in the critical theory.

#### Article information

Source
Taiwanese J. Math., Volume 19, Number 4 (2015), 1215-1226.

Dates
First available in Project Euclid: 4 July 2017

https://projecteuclid.org/euclid.twjm/1499133697

Digital Object Identifier
doi:10.11650/tjm.19.2015.4716

Mathematical Reviews number (MathSciNet)
MR3384687

Zentralblatt MATH identifier
1357.35113

#### Citation

Xu, Liping; Chen, Haibo. MULTIPLE SOLUTIONS FOR THE NONHOMOGENEOUS FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE. Taiwanese J. Math. 19 (2015), no. 4, 1215--1226. doi:10.11650/tjm.19.2015.4716. https://projecteuclid.org/euclid.twjm/1499133697

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