A note on nonlinear elliptic problems with singular potentials

DOI10.4171/RLM/450zbMath1126.35021MaRDI QIDQ2504827

Sergio Rolando, Marino Badiale

Publication date: 1 February 2007

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: http://www.ems-ph.org/journals/show_abstract.php?issn=1120-6330&vol=17&iss=1&rank=1

zbMATH Keywords

Semilinear elliptic equationradial solutionsingular potential

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (24)

Weighted Sobolev embedding with unbounded and decaying radial potentials ⋮ Nehari–Pohožaev-type ground state solutions of Kirchhoff-type equation with singular potential and critical exponent ⋮ Pohožaev-type ground state solutions for Choquard equation with singular potential and critical exponent ⋮ Multiple nonradial solutions for a nonlinear elliptic problem with singular and decaying radial potential ⋮ Sobolev type embedding and quasilinear elliptic equations with radial potentials ⋮ Existence of ground‐state solutions for p‐Choquard equations with singular potential and doubly critical exponents ⋮ Lions-type properties for the \(p\)-Laplacian and applications to quasilinear elliptic equations ⋮ Critical Kirchhoff-type equation with singular potential ⋮ Existence and multiplicity of solutions for critical elliptic equations with multi-polar potentials in symmetric domains ⋮ Sum of weighted Lebesgue spaces and nonlinear elliptic equations ⋮ Nonlinear biharmonic problems with singular potentials ⋮ Quasilinear Schrödinger equations with a positive parameter and involving unbounded or decaying potentials ⋮ Compactness and existence results in weighted Sobolev spaces of radial functions. I: Compactness ⋮ A nonlinear elliptic equation with singular potential and applications to nonlinear field equations ⋮ Radial nonlinear elliptic problems with singular or vanishing potentials ⋮ Positive solution to Schrödinger equation with singular potential and double critical exponents ⋮ Lions-type theorem of the \(p\)-Laplacian and applications ⋮ Ground state solution of critical Schrödinger equation with singular potential ⋮ Ground state solutions for nonlinear Choquard equation with singular potential and critical exponents ⋮ Multiple nonradial solutions for a nonlinear elliptic radial problem: an improved result ⋮ Unnamed Item ⋮ Nonlinear elliptic equations with subhomogeneous potentials ⋮ Fractional Sobolev embedding with radial potential ⋮ Ground state solutions for critical Choquard equation with singular potential: existence and regularity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The principle of symmetric criticality
• Nonlinear scalar field equations. I: Existence of a ground state
• Existence of solitary waves in higher dimensions
• Infinitely many radial solutions of a semilinear elliptic problem on \(\mathbb{R}^ N\)
• Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type.
• On positive entire solutions to a class of equations with a singular coefficient and critical exponent
• On the existence of positive solutions for a class of singular elliptic equations
• Dual variational methods in critical point theory and applications
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• Nodal solutions to a class of nonstandard superlinear equations on \(\mathbb R^ N\).

This page was built for publication: A note on nonlinear elliptic problems with singular potentials