## Taiwanese Journal of Mathematics

### Existence of Nonnegative Solutions for Fourth Order Elliptic Equations of Kirchhoff Type with General Subcritical Growth

#### Abstract

This paper is dedicated to investigating the following fourth-order elliptic equation with Kirchhoff-type $\begin{cases} \displaystyle \Delta^{2} u - \left( a + b \int_{\mathbb{R}^{N}} |\nabla u|^{2} \, dx \right) \Delta u + cu = f(u) &\textrm{in \mathbb{R}^{N}}, \\ u \in H^{2}(\mathbb{R}^{N}), \end{cases}$ where $a \gt 0$, $b \geq 0$ and $c \gt 0$ are constants. By using cut-off functional and monotonicity tricks, we prove that the above problem has a positive solution. Our result cover the case where the nonlinearity satisfies asymptotically linear and superlinear condition at the infinity, which extend the results of related literatures.

#### Article information

Source
Taiwanese J. Math., Advance publication (2019), 16 pages.

Dates
First available in Project Euclid: 26 February 2019

https://projecteuclid.org/euclid.twjm/1551150032

Digital Object Identifier
doi:10.11650/tjm/190202

#### Citation

Huang, Jianping; Zhang, Qi. Existence of Nonnegative Solutions for Fourth Order Elliptic Equations of Kirchhoff Type with General Subcritical Growth. Taiwanese J. Math., advance publication, 26 February 2019. doi:10.11650/tjm/190202. https://projecteuclid.org/euclid.twjm/1551150032

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