Multiple solutions of a quasilinear elliptic system involving the nonlinear boundary conditions on exterior domain |
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Authors: | Shuai Liu Caisheng Chen |
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Institution: | College of Science, Hohai University, , Nanjing, Jiangsu Province, 210098 China |
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Abstract: | In this paper, we consider the multiplicity results of nontrivial nonnegative solutions of the quasilinear p‐Laplacian system with the nonlinear boundary conditions: (0.1) where Ω is a smooth exterior domain in is the outward normal derivative on the boundary Γ = ?Ω, and . By the Nehari manifold and variational methods, we prove that the problem (0.1) has at least two nontrivial nonnegative solutions when the pair of the parameters (λ,μ) belongs to a certain subset of . Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | quasilinear p‐Laplacian system Nehari manifold variational methods nonlinear boundary conditions lack of compactness |
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