Special Issue in honor of Alan C. Lazer. Electron. J. Diff. Eqns., Special Issue 01 (2021), pp. 239-253.

Connected components of positive solutions of biharmonic equations with the clamped plate conditions in two dimensions

Ruyun Ma, Zhongzi Zhao, Dongliang Yan

Abstract:
This article concerns the clamped plate equation

where $\Omega$ is a bounded domain in $\mathbb{R}^2$ of class $C^{4, \alpha}$, $a\in C(\bar \Omega, (0, \infty))$, $f: [0, \infty)\to [0,\infty)$ is a locally Hölder continuous function with exponent $\alpha$, and $\lambda$ is a positive parameter. We show the existence of S-shaped connected component of positive solutions under suitable conditions on the nonlinearity. Our approach is based on bifurcation techniques.

Published November 03, 2021.
Math Subject Classifications: 35J40, 35G30, 35B32, 35P30.
Key Words: Biharmonic operator; positive solutions; eigenvalue; bifurcation.
DOI: https://doi.org/10.58997/ejde.sp.01.m1

Show me the PDF file (387 K), TEX file for this article.

Ruyun Ma
School of Mathematics and Statistics
Xidian University, Xi'an 710071, China
email: ryma@xidian.edu.cn
Zhongzi Zhao
School of Mathematics and Statistics
Xidian University, Xi'an 710071, China
email: 15193193403@163.com
Dongliang Yan
Department of Mathematics
Northwest Normal University
Lanzhou 730070, China
email: yhululu@163.com

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