A perturbation theorem for the equation −Δu + λu = uP in unbounded domains

DOI10.1016/S0362-546X(96)00080-6zbMath0872.35040MaRDI QIDQ3124195

Andrea Dall'Aglio, Massimo Grossi

Publication date: 15 October 1997

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

existenceconcentration-compactness methodperturbation of unbounded domains

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Singular perturbations in context of PDEs (35B25) Variational methods for second-order elliptic equations (35J20)

Related Items

A perturbation theorem for the \(p\)-Laplace equation in unbounded domains ⋮ Nontrivial solutions for Neumann problems with an indefinite linear part ⋮ Existence of positive solutions for some nonlinear elliptic equations on unbounded domains with cylindrical ends. ⋮ Calculus of variations for a boundary value problem of differential system on the half line ⋮ On a semilinear elliptic equation with indefinite linear part

Cites Work

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• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• On a min-max procedure for the existence of a positive solution for certain scalar field equations in \({\mathbb{R}}^ N\)
• Positive solutions of some nonlinear elliptic problems in exterior domains
• On the existence of a positive solution of semilinear elliptic equations in unbounded domains
• An existence result for a semilinear equation in some domains with unbounded boundary
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• A Note on an Equation with Critical Exponent
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Existence and multiplicity of positive solutions for nonlinear elliptic problems in exterior domains with “rich” topology
• Semilinear elliptic problems with singular potentials in ℝ^N
• Existence and non-existence results for semilinear elliptic problems in unbounded domains
• A compactness lemma