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2014 Multiplicity of Positive Solutions for a p-q-Laplacian Type Equation with Critical Nonlinearities
Tsing-San Hsu, Huei-Li Lin
Abstr. Appl. Anal. 2014(none): 1-9 (2014). DOI: 10.1155/2014/829069

Abstract

We study the effect of the coefficient f(x) of the critical nonlinearity on the number of positive solutions for a p-q-Laplacian equation. Under suitable assumptions for f(x) and g(x), we should prove that for sufficiently small λ>0, there exist at least k positive solutions of the following p-q-Laplacian equation, -Δpu-Δqu=fxu|p*-2u+λgxu|r-2u in Ω, u=0 on Ω, where ΩRN is a bounded smooth domain, N>p, 1<q<N(p-1)/(N-1)<pmax{p,p^*-q/(p-1)}<r<p^*, p^*=Np/(N-p) is the critical Sobolev exponent, and Δsu=div(|u|s-2u is the s-Laplacian of u.

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Tsing-San Hsu. Huei-Li Lin. "Multiplicity of Positive Solutions for a p-q-Laplacian Type Equation with Critical Nonlinearities." Abstr. Appl. Anal. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/829069

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023153
MathSciNet: MR3193552
Digital Object Identifier: 10.1155/2014/829069

Rights: Copyright © 2014 Hindawi

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