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Multiplicity of solutions to the weighted critical quasilinear problems

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  04 January 2012

Sihua Liang  and
Jihui Zhang
Sihua Liang
Affiliation:
Department of Mathematics, Changchun Normal University, Changchun 130032, Jilin, People's Republic of China (liangsihua@163.com)
Jihui Zhang
Affiliation:
Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing, Jiangsu 210046, People's Republic of China
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Abstract

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We consider a class of critical quasilinear problems

where 0 ∈ Ω ⊂ ℝN, N ≥ 3, is a bounded domain and 1 < p < N, a < N/p, a ≤ b < a + 1, λ is a positive parameter, 0 ≤ μ < ≡ ((N − p)/p − a)p, q = q*(a, b) ≡ Np/[N − pd] and d ≡ a+1 − b. Infinitely many small solutions are obtained by using a version of the symmetric Mountain Pass Theorem and a variant of the concentration-compactness principle. We deal with a problem that extends some results involving singularities not only in the nonlinearities but also in the operator.

Keywords

degenerate quasilinear equationp-Laplacian operatorvariational methodsconcentration-compactness principle

MSC classification

Secondary: 35J60: Nonlinear elliptic equations 35B33: Critical exponents 35J65: Nonlinear boundary value problems for linear elliptic equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 181 - 195
Copyright
Copyright © Edinburgh Mathematical Society 2011

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