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February, 2020 Existence of Nonnegative Solutions for Fourth Order Elliptic Equations of Kirchhoff Type with General Subcritical Growth
Jianping Huang, Qi Zhang
Taiwanese J. Math. 24(1): 81-96 (February, 2020). DOI: 10.11650/tjm/190202

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.

Citation

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Jianping Huang. Qi Zhang. "Existence of Nonnegative Solutions for Fourth Order Elliptic Equations of Kirchhoff Type with General Subcritical Growth." Taiwanese J. Math. 24 (1) 81 - 96, February, 2020. https://doi.org/10.11650/tjm/190202

Information

Received: 12 September 2017; Revised: 18 July 2018; Accepted: 17 February 2019; Published: February, 2020
First available in Project Euclid: 26 February 2019

zbMATH: 07175541
MathSciNet: MR4053839
Digital Object Identifier: 10.11650/tjm/190202

Subjects:
Primary: 35J35 , 35J50 , 35J60

Keywords: cut-off functional , fourth order elliptic equations , Pohožaev equality

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 1 • February, 2020
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