Limits as p → ∞ of p-laplacian eigenvalue problems perturbed with a concave or convex term
Charro, Fernando; Parini, Enea (2013), Limits as p → ∞ of p-laplacian eigenvalue problems perturbed with a concave or convex term, Calculus of Variations and Partial Differential Equations, 46, 1-2, p. 403-425. http://dx.doi.org/10.1007/s00526-011-0487-7
TypeArticle accepté pour publication ou publié
Journal nameCalculus of Variations and Partial Differential Equations
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Abstract (EN)We investigate the asymptotic behaviour as p → ∞ of sequences of positive weak solutions of the equation −pu=up−1+uq(p)−1inu=0on where λ > 0 and either 1 < q(p) < p or p < q(p), with limpq(p)p=Q=1 . Uniform limits are characterized as positive viscosity solutions of the problem minu(x)−maxu(x)uQ(x)−u(x)=0inu=0on for appropriate values of Λ > 0. Due to the decoupling of the nonlinearity under the limit process, the limit problem exhibits an intermediate behavior between an eigenvalue problem and a problem with a power-like right-hand side. Existence and non-existence results for both the original and the limit problems are obtained.
Subjects / KeywordsPDEs
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Limits as p→∞ of p-Laplacian problems with a superdiffusive power-type nonlinearity: Positive and sign-changing solutions Parini, Enea; Charro, Fernando (2010) Article accepté pour publication ou publié