On the Morse critical groups for indefinite sublinear elliptic problems
type: Item
instance of: scholarly article
title: On the Morse critical groups for indefinite sublinear elliptic problems
zbMATH Open document ID: 1087.35040
DOI: 10.1016/S0362-546X(02)00174-8
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: The author studies a parameter dependent semilinear Dirichlet problem with weight by methods of infinite dimensional Morse theory. Specifically, it is shown that, if a parameter in the problem is not too large, the Morse critical groups at zero for the associated energy functional are trivial. This implies the existence of a nontrivial solution when some nonlinear term in the problem is asymptotically linear. Then the bifurcation of small solutions is obtained under the assumption that a parameter related to the weight is sufficiently small.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 1880104
zbMATH Keywords: sublinear elliptic equations
zbMATH Keywords: indefinite weights
zbMATH Keywords: nontrivial solutions
zbMATH Keywords: bifurcation
zbMATH Keywords: Morse theory
zbMATH Keywords: Morse critical groups
author: Vitaly Moroz
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
cites work: Semilinear elliptic equations with sublinear indefinite nonlinearities
cites work: Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking
cites work: Combined effects of concave and convex nonlinearities in some elliptic problems
cites work: Multiplicity results for some nonlinear elliptic equations
cites work: The Asymptotic Behavior of the Solutions of Degenerate Parabolic Equations
cites work: Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
cites work: On the existence of sign changing solutions for semilinear Dirichlet problems
cites work: Infinite dimensional Morse theory and multiple solution problems
cites work: The Conley index and the critical groups via an extension of Gromoll-Meyer theory
cites work: The generalized Conley index and multiple solutions of semilinear elliptic problems
cites work: Continuous domain dependence of the eigenvalues of the Dirichlet Laplacian and related operators in Hilbert space
cites work: Multiple solutions for a class of semilinear elliptic equations
cites work: Mountain pass theorem in order intervals and multiple solutions for semilinear elliptic Dirichlet problems
cites work: Critical point theory and Hamiltonian systems
cites work: Q3771277
cites work: Solutions of superlinear at zero elliptic equations via Morse theory
cites work: Q3992017
cites work: Critical groups of pairs of critical points produced by linking subsets
cites work: Support properties of solutions for a class of degenerate parabolic problems
cites work: Q5522742
cites work: Nonlinear boundary value problems with concave nonlinearities near the origin
description: scientific article; zbMATH DE number 1880104