Seven solutions with sign information for sublinear equations with unbounded and indefinite potential and no symmetries
type: Item
instance of: scholarly article
title: Seven solutions with sign information for sublinear equations with unbounded and indefinite potential and no symmetries
zbMATH Open document ID: 1310.35135
author: Nikolaos S. Papageorgiou
author: Francesca Papalini
published in: Israel Journal of Mathematics
publication date: 2014-10-24T00:00:00Z
review text: In this paper, the Dirichlet problem: \[ \begin{cases} -\Delta u(z) + \beta(z)u(z) = f(z,u(z)) \quad \text{in} \;\Omega, \\ u|_{\partial \Omega} = 0 \end{cases} \] is considered, where \(\Omega \subset {\mathbb R}^N\) is a bounded domain with a \(C^2\)-boundary \(\partial \Omega\), \(N \geq 3\), \(\beta \in L^s(\Omega)\), \(s>N\) and, in general, it is indefinite (sign changing) and unbounded from below. It is shown that the problem has at least seven nontrivial smooth solutions and provide sign information for all of them.
reviewed by: Satoshi Tanaka
Mathematics Subject Classification ID: 35J91
zbMATH DE Number: 6361316
MaRDI profile type: Publication
full work available at URL: s11856-014-1050-y
OpenAlex ID: W2008700620
cites work: Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints
cites work: Critical point theory on partially ordered Hilbert spaces
cites work: Q3140494
cites work: Existence of seven solutions for an asymptotically linear Dirichlet problem without symmetries
cites work: Critical point theory and the number of solutions of a nonlinear Dirichlet problem
cites work: Morse theory for indefinite nonlinear elliptic problems
cites work: Variational elliptic problems which are nonquadratic at infinity
cites work: A note on multiple solutions of some semilinear elliptic problems
cites work: Q3254057
cites work: On periodic solutions of superquadratic Hamiltonian systems
cites work: Strict Monotonicity of Eigenvalues and Unique Continuation
cites work: Unique continuation for elliptic operators: A geometric-variational approach
cites work: Q5312447
cites work: Nodal and multiple constant sign solutions for resonant \(p\)-Laplacian equations with a nonsmooth potential
cites work: Multiple solutions for superlinear Dirichlet problems with an indefinite potential
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: Homotopy theory of infinite dimensional manifolds
cites work: Constant sign and nodal solutions for logistic-type equations with equidiffusive reaction
cites work: Multiple solutions for nearly resonant nonlinear Dirichlet problems
cites work: The maximum principle
cites work: Multiple solutions of superlinear elliptic equations
cites work: Q3997570
cites work: Semilinear elliptic boundary value problems with double resonance between two consecutive eigenvalues
cites work: A strong maximum principle for some quasilinear elliptic equations
cites work: On a superlinear elliptic equation
DOI: 10.1007/S11856-014-1050-Y
description: scientific article; zbMATH DE number 6361316