Limits as \(p\rightarrow\infty \) of \(p\)-Laplacian problems with a superdiffusive power-type nonlinearity: positive and sign-changing solutions

DOI10.1016/j.jmaa.2010.07.005zbMath1198.35115arXiv1405.0621OpenAlexW1968507122MaRDI QIDQ994334

Fernando Charro, Enea Parini

Publication date: 17 September 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.0621

zbMATH Keywords

viscosity solution\(p\)-LaplacianMorrey's estimate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Quasilinear elliptic equations (35J62) Viscosity solutions to PDEs (35D40) Positive solutions to PDEs (35B09) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (11)

Existence of nonnegative viscosity solutions for a class of problems involving the \(\infty\)-Laplacian ⋮ The convergence of nonnegative solutions for the family of problems −Δ_pu=λe^uasp→∞ ⋮ Minimization problems for inhomogeneous Rayleigh quotients ⋮ Limits as \(p \rightarrow \infty \) of \(p\)-Laplacian eigenvalue problems perturbed with a concave or convex term ⋮ Limits as \(p\to \infty \) of \(p\)-Laplacian concave-convex problems ⋮ The Gelfand problem for the infinity Laplacian ⋮ On the monotonicity of the principal frequency of the \(p\)-Laplacian ⋮ On the behavior of least energy solutions of a fractional ( p , q ( p ) )-Laplacian problem as p goes to infinity ⋮ Asymptotic behavior of extremals for fractional Sobolev inequalities associated with singular problems ⋮ Asymptotic behaviour asp→ ∞ of least energy solutions of a (p, q(p))-Laplacian problem ⋮ The limiting behavior of constrained minimizers in Orlicz-Sobolev spaces

Cites Work

• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• On the asymptotics of solutions of the Lane-Emden problem for the \(p\)-Laplacian
• On the higher eigenvalues for the \(\infty\)-eigenvalue problem
• The \(\infty\)-eigenvalue problem
• A direct uniqueness proof for equations involving the \(p\)-Laplace operator
• Limit as \(p\to \infty \) of \(p\)-Laplace eigenvalue problems and \(L^\infty \)-inequality of the Poincaré type.
• Limit Branch of Solutions asp → ∞ for a Family of Sub-Diffusive Problems Related to thep-Laplacian
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