Multiple solutions of a quasilinear elliptic problem involving nonlinear boundary condition on exterior domain |
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Authors: | Caisheng Chen Qi Zhang |
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Institution: | College of Science, Hohai University Nanjing 210098, , Jiangsu Province, China |
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Abstract: | In this paper, we study the multiplicity of non‐negative solutions for the quasilinear p‐Laplacian equation with the nonlinear boundary condition (1) where Δp denotes the p‐Laplacian operator, defined by △ pu = div( | ? u | p ? 2 ? u),1 < p < N, Ω is a smooth exterior domain in . is the outward normal derivative, . The parameters p,q,r are either or . The weight functions a(x),h(x),g(x) satisfy some suitable conditions. Using the decomposition of the Nehari manifold and the variational methods, we prove that problem (1) has at least two positive solutions provided 0 < | λ | < λ1 for some λ1. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | quasilinear elliptic problem p‐Laplacian equation Nehari manifold nonlinear boundary condition |
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