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2018 On a class of singular superlinear elliptic systems in a ball
Dang Dinh Hai
Tohoku Math. J. (2) 70(3): 339-352 (2018). DOI: 10.2748/tmj/1537495350

Abstract

We establish the existence of large positive radial solutions for the elliptic system $$ \left\{ \begin{array}{c} -\Delta u=\lambda f(v) \ \text{in} \ B\\ -\Delta v=\lambda g(u) \ \text{in} \ B\\ u=v=0 \ \text{on} \ \partial B \end{array} \right. $$ when the parameter $\lambda>0$ is small, where $B$ is the open unit ball $\mathbb{R}^N,N>2, f,g:(0,\infty) \rightarrow \mathbb{R}$ are possibly singular at 0 and $f(u) \sim u^p,g(v) \sim v^q$ at $\infty$ for some $p,q>0$ with $pq>1$. Our approach is based on fixed point theory in a cone.

Citation

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Dang Dinh Hai. "On a class of singular superlinear elliptic systems in a ball." Tohoku Math. J. (2) 70 (3) 339 - 352, 2018. https://doi.org/10.2748/tmj/1537495350

Information

Published: 2018
First available in Project Euclid: 21 September 2018

zbMATH: 06996531
MathSciNet: MR3856770
Digital Object Identifier: 10.2748/tmj/1537495350

Subjects:
Primary: 35J57
Secondary: 35J75

Keywords: positive radial solutions , singular elliptic systems

Rights: Copyright © 2018 Tohoku University

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Vol.70 • No. 3 • 2018
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