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February 2010 On positive solutions for $p$-Laplacian systems with sign-changing nonlinearities
Dang Dinh HAI
Hokkaido Math. J. 39(1): 67-84 (February 2010). DOI: 10.14492/hokmj/1274275020

Abstract

We consider the existence and multiplicity of positive solutions to the quasilinear system $$ \begin{cases} -\Delta_{p_{i}}u_{i} = \mu_{i}a_{i}(x)f_{i}(u_{1},\dots,u_{n})~\text{in}~\Omega,\;i=1,\dots,n, \\[1pt] u_{i} = 0~\text{on}~\partial \Omega , \end{cases} $$ where $\Omega$ is a bounded domain in $\mathbb{R}^{N}$ with a smooth boundary $\partial \Omega$, $\Delta_{p_{i}}u_{i}={\rm div}(|\nabla u_{i}|^{p_{i}-2}\nabla u_{i})$, $p_{i}>1$, $\mu_{i}$ are positive parameters, and $f_{i}$ are allowed to change sign.

Citation

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Dang Dinh HAI. "On positive solutions for $p$-Laplacian systems with sign-changing nonlinearities." Hokkaido Math. J. 39 (1) 67 - 84, February 2010. https://doi.org/10.14492/hokmj/1274275020

Information

Published: February 2010
First available in Project Euclid: 19 May 2010

zbMATH: 1196.35084
MathSciNet: MR2649327
Digital Object Identifier: 10.14492/hokmj/1274275020

Subjects:
Primary: 35J55
Secondary: 35J60

Rights: Copyright © 2010 Hokkaido University, Department of Mathematics

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Vol.39 • No. 1 • February 2010
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