Spectral density estimates with partial symmetries and an application to Bahri-Lions-type results
type: Item
instance of: scholarly article
title: Spectral density estimates with partial symmetries and an application to Bahri-Lions-type results
zbMATH Open document ID: 1372.35078
author: Nils Ackermann
author: Alfredo Cano
author: Eric Hernández-Martínez
published in: Calculus of Variations and Partial Differential Equations
publication date: 2017-04-13T00:00:00Z
review text: The boundary value problem \(-\Delta u=|u|^{p-2}u+f\) in \(\Omega\), \(u=u_0\) on \(\partial \Omega\), where \(\Omega\) is a domain in \(\mathbb R^N\) (\(N\geq 3\)) with a sufficiently smooth boundary \(\partial \Omega\), is discussed. The authors consider conditions on \(p\), \(f\) and \(u_0\) when the problem has infinitely many solutions extending the known results for \(f=0\) and \(u_0=0\). The authors determine the maximal possible \(p\) employing improved Sobolev embeddings for spaces of invariant functions. Spectral density estimates for Schrödinger operators are used.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J61
zbMATH DE Number: 6705789
zbMATH Keywords: Laplace operator
zbMATH Keywords: boundary value problems
zbMATH Keywords: infinitely many solutions
reviewed by: Vladimir Mityushev
MaRDI profile type: Publication
full work available at URL: s00526-016-1107-3
OpenAlex ID: W2569087200
cites work: Morse index of some min-max critical points. I. Application to multiplicity results
cites work: Morse indices at critical points related to the symmetric mountain pass theorem and applications
cites work: A Perturbation Method in Critical Point Theory and Applications
cites work: Multiple Critical Points of Perturbed Symmetric Functionals
cites work: Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems
cites work: Topological results on a certain class of functionals and application
cites work: Infinitely many solutions for a perturbed Schrödinger equation
cites work: A perturbation method for multiple sign-changing solutions
cites work: Nodal solutions of a perturbed elliptic problem
cites work: Perturbations from symmetric elliptic boundary value problems
cites work: Multiple solutions for perturbed indefinite semilinear elliptic equations.
cites work: Perturbation from symmetry and multiplicity of solutions for elliptic problems with subcritical exponential growth in \(\mathbb R^2\)
cites work: Infinitely many solutions for indefinite semilinear elliptic equations without symmetry
cites work: Existence of infinitely many critical values of some nonsymmetric functionals
cites work: Multiple Solutions for Perturbed Elliptic Equations in Unbounded Domains
cites work: The multiplicity of solutions in non-homogeneous boundary value problems
cites work: Multiplicity results of an elliptic equation with non-homogeneous boundary conditions
cites work: Superlinear elliptic boundary value problems with rotational symmetry
cites work: Infinitely Many Radially Symmetric Solutions to a Superlinear Dirichlet Problem in a Ball
cites work: Remarks on some quasilinear elliptic equations
cites work: Radial solutions of semilinear elliptic equations with broken symmetry
cites work: Multiplicity results for some perturbed elliptic problems in unbounded domains with non-homogeneous boundary conditions
cites work: Radial solutions of semilinear elliptic equations with broken symmetry on unbounded domains
cites work: Infinitely Many Solutions of Elliptic Problems With Perturbed Symmetries in Symmetric Domains
cites work: Representations of compact Lie groups and elliptic operators
cites work: \(G\)-spaces, the asymptotic splitting of \(L^2(M)\) into irreducibles
cites work: Multiplicity Results for some Perturbed and Unperturbed “Zero Mass” Elliptic Problems in Unbounded Cylinders
cites work: On the Bolza problem
cites work: On the Schrödinger equation and the eigenvalue problem
cites work: New estimates on the number of bound states of Schrödinger operators
cites work: Sobolev spaces in the presence of symmetries
cites work: Sobolev embeddings involving symmetry
cites work: Bounds on the eigenvalues of the Laplace and Schroedinger operators
cites work: Weak type estimates for singular values and the number of bound states of Schrödinger operators
cites work: Q5662833
cites work: On the Number of Bound States in a Central Field of Force
cites work: A short proof for Bargmann–type inequalities
cites work: Linking--preserving perturbations of symmetric functionals.
cites work: Q3749777
cites work: Q4340096
cites work: Q4041031
cites work: Eigenvalue distribution of compact operators
cites work: Q5187597
DOI: 10.1007/S00526-016-1107-3
description: scientific article; zbMATH DE number 6705789