PERTURBING SINGULAR SOLUTIONS OF THE GELFAND PROBLEM

DOI10.1142/S0219199707002575zbMath1154.35047MaRDI QIDQ5386892

Juan Dávila, Louis Dupaigne

Publication date: 14 May 2008

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

singular solutionsnonlinear elliptic equationsGelfand problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Stability in context of PDEs (35B35) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (19)

Singular solutions of Toda system in high dimensions ⋮ Singular solutions of a \(p\)-Laplace equation involving the gradient ⋮ The Gelfand problem on annular domains of double revolution with monotonicity ⋮ Singular solutions of elliptic equations involving nonlinear gradient terms on perturbations of the ball ⋮ A nonlinear elliptic problem involving the gradient on a half space ⋮ Supercritical elliptic problems on a perturbation of the ball ⋮ Singular solutions of elliptic equations on a perturbed cone ⋮ Fundamental properties and asymptotic shapes of the singular and classical radial solutions for supercritical semilinear elliptic equations ⋮ Sharp estimates of radial minimizers of 𝑝–Laplace equations ⋮ Singular solutions of a Lane-Emden system ⋮ Singular solutions of elliptic equations with iterated exponentials ⋮ Asymptotic profile and Morse index of nodal radial solutions to the Hénon problem ⋮ Supercritical elliptic problems involving a Cordes like operator ⋮ Some elliptic problems involving the gradient on general bounded and exterior domains ⋮ Regularity of radial minimizers of reaction equations involving the \(p\)-Laplacian ⋮ Singular solutions of a Hénon equation involving a nonlinear gradient term ⋮ Stable and finite Morse index solutions of Toda system ⋮ Topics of stable solutions to elliptic equations ⋮ Singular extremal solutions to a Liouville-Gelfand type problem with exponential nonlinearity

Cites Work

• A construction of singular solutions for a semilinear elliptic equation using asymptotic analysis
• A nonlinear elliptic PDE with the inverse square potential.
• Regularity of radial minimizers and extremal solutions of semilinear elliptic equations
• Minimal surfaces with isolated singularities
• Conformally flat metrics of constant positive scalar curvature on subdomains of the sphere
• Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
• Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
• Construction of singular limits for a semilinear elliptic equation in dimension 2
• The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential
• Weak solutions of nonlinear elliptic equations with prescribed singular set
• Sur une classe de problemes non lineaires avec non linearite positive, croissante, convexe.
• Solutions of semilinear elliptic equations with many isolated singularities: the unstable case
• Comparison results for PDEs with a singular potential
• Some problems in the theory of quasilinear equations

This page was built for publication: PERTURBING SINGULAR SOLUTIONS OF THE GELFAND PROBLEM