Some Results for the Gelfand's Problem

DOI10.1081/PDE-200037754zbMath1140.35417MaRDI QIDQ3157929

Massimo Grossi, Francesca Gladiali

Publication date: 20 January 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

qualitative propertiesGelfand problem

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45)

Related Items (19)

On the number of critical points of solutions of semilinear equations in ℝ2 ⋮ Blow-up analysis for Neri's mean field equation in 2D-turbulence ⋮ Morse Indices of Multiple Blow-Up Solutions to the Two-Dimensional Gel'fand Problem ⋮ Local and global behavior of solutions to 2 D-elliptic equation with exponentially-dominated nonlinearities ⋮ Morse indices of the solutions to the inhomogeneous elliptic equation with exponentially dominated nonlinearities ⋮ Non degeneracy of critical points of the Robin function with respect to deformations of the domain ⋮ Uniqueness of bubbling solutions of mean field equations ⋮ Uniqueness of the critical point for semi-stable solutions in \(\mathbb{R}^2\) ⋮ Asymptotic behavior of minimal solutions of \(-\Delta u=\lambda f(u)\) as \(\lambda\to-\infty\) ⋮ On the shape of level sets of least energy solutions to some elliptic problems with nearly critical growth ⋮ Local uniqueness of m-bubbling sequences for the Gel’fand equation ⋮ Nonexistence of multi-bubble solutions to some elliptic equations on convex domains ⋮ Non-uniqueness of blowing-up solutions to the Gelfand problem ⋮ Non-degeneracy, mean field equations and the Onsager theory of 2D turbulence ⋮ On the spectrum of a nonlinear planar problem ⋮ A Morse lemma for degenerate critical points of solutions of nonlinear equations in \(\mathbb{R}^2\) ⋮ Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains ⋮ Morse Indices of the Solutions to the Liouville-Gel'fand Problem with Variable Coefficients ⋮ Uniqueness of bubbling solutions of mean field equations with non-quantized singularities

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