The Gelfand problem for the infinity Laplacian

DOI10.3934/mine.2023022arXiv2112.09247OpenAlexW4225693753WikidataQ114022464 ScholiaQ114022464MaRDI QIDQ6195562

Byungjae Son, Fernando Charro, Pei-Yong Wang

Publication date: 14 March 2024

Published in: Mathematics in Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.09247

zbMATH Keywords

infinity Laplacianfully nonlinearGelfand problem

Mathematics Subject Classification ID

Ordinary differential equations (34-XX) Elliptic equations and elliptic systems (35Jxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of nonnegative viscosity solutions for a class of problems involving the \(\infty\)-Laplacian
• Limits as \(p\to \infty \) of \(p\)-Laplacian concave-convex problems
• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• The Liouville-Bratu-Gelfand problem for radial operators
• Principal eigenvalue of a very badly degenerate operator and applications
• Limits as \(p\rightarrow\infty \) of \(p\)-Laplacian problems with a superdiffusive power-type nonlinearity: positive and sign-changing solutions
• On the higher eigenvalues for the \(\infty\)-eigenvalue problem
• The \(\infty\)-eigenvalue problem
• Surfaces with prescribed Gauss curvature
• Limit as \(p\to \infty \) of \(p\)-Laplace eigenvalue problems and \(L^\infty \)-inequality of the Poincaré type.
• Limits as \(p \rightarrow \infty \) of \(p\)-Laplacian eigenvalue problems perturbed with a concave or convex term
• Regularity of the extremal solution of some nonlinear elliptic problems involving the \(p\)-Laplacian
• Semi-stable and extremal solutions of reaction equations involving the \(p\)-Laplacian
• Multiple bubbling for the exponential nonlinearity in the slightly supercritical case
• Existence and nonexistence results for quasilinear elliptic equations involving the \(p\)-Laplacian with a critical potential
• Quasilinear Dirichlet problems driven by positive sources
• \(p\)-Laplace operator and diameter of manifolds
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
• On a familiy of torsional creep problems.
• Remarks on sublinear elliptic equations
• User’s guide to viscosity solutions of second order partial differential equations
• Addendum to On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0"
• On an Emden-Fowler type equation
• Quasilinear problems with exponential growth in the reaction term
• The convergence of nonnegative solutions for the family of problems −Δ_pu=λe^uasp→∞
• On the Existence of Positive Solutions of Semilinear Elliptic Equations
• Some properties of the ground states of the infinity Laplacian
• Some problems in the theory of quasilinear equations
• Limit Branch of Solutions asp → ∞ for a Family of Sub-Diffusive Problems Related to thep-Laplacian