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2018 Existence of solutions for the semilinear corner degenerate elliptic equations
Jae-Myoung Kim
Topol. Methods Nonlinear Anal. 52(2): 585-597 (2018). DOI: 10.12775/TMNA.2018.021

Abstract

In this paper, we are concerned with the following elliptic equations: \begin{equation*}\label{e:JG} \begin{cases} -\Delta_{\mathbb{M}}u = \lambda f &\text{in } z:= (r,x,t) \in \mathbb{M}_0,\\ u= 0 &\text{on } \partial\mathbb{M}. \end{cases} \end{equation*} Here, $\lambda >0$ and $M=[0,1)\times X\times[0,1)$ as a local model of stretched corner-manifolds, that is, the manifolds with corner singularities with dimension $N=n+2\geq 3$. Here $X$ is a closed compact submanifold of dimension $n$ embedded in the unit sphere of $\mathbb{R}^{n+1}$. We study the existence of nontrivial weak solutions for the semilinear corner degenerate elliptic equations without the Ambrosetti and Rabinowitz condition via the mountain pass theorem and fountain theorem.

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Jae-Myoung Kim. "Existence of solutions for the semilinear corner degenerate elliptic equations." Topol. Methods Nonlinear Anal. 52 (2) 585 - 597, 2018. https://doi.org/10.12775/TMNA.2018.021

Information

Published: 2018
First available in Project Euclid: 6 November 2018

zbMATH: 07051681
MathSciNet: MR3915652
Digital Object Identifier: 10.12775/TMNA.2018.021

Rights: Copyright © 2018 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.52 • No. 2 • 2018
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