Critical and subcritical fractional problems with vanishing potentials

DOI10.1142/S0219199715500637zbMath1348.35152arXiv1410.0843OpenAlexW1888115680MaRDI QIDQ2828647

Marco Squassina, Olímpio Hiroshi Miyagaki, João Marcos Bezerra do Ó

Publication date: 26 October 2016

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.0843

zbMATH Keywords

variational methodsfractional Laplacianvanishing potentialsnonautonomous equations

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Estimates of eigenvalues in context of PDEs (35P15) Fractional partial differential equations (35R11)

Related Items (37)

Solutions for a class of fractional Hamiltonian systems with exponential growth ⋮ Positive solutions for a class of fractional \(p\)-Laplacian equation with critical Sobolev exponent and decaying potentials ⋮ Elliptic problem driven by different types of nonlinearities ⋮ Existence of infinitely many high energy solutions for a fractional Schrödinger equation in \(\mathbb{R}^N\) ⋮ Singularly perturbed fractional Schrödinger equations with critical growth ⋮ Three solutions for a fractional Schrödinger equation with vanishing potentials ⋮ Functional convergence of continuous-time random walks with continuous paths ⋮ Existence of positive solutions for a critical fractional Kirchhoff equation with potential vanishing at infinity ⋮ Ground state solutions for a class of fractional Kirchhoff equations with critical growth ⋮ Fractional Schrödinger equations involving potential vanishing at infinity and supercritical exponents ⋮ Asymptotic behavior of ground states and local uniqueness for fractional Schrödinger equations with nearly critical growth ⋮ Critical and subcritical fractional Hamiltonian systems of Schrödinger equations with vanishing potentials ⋮ One‐dimensional periodic fractional Schrödinger equations with exponential critical growth ⋮ On a nonlocal elliptic system of Hardy‐Kirchhoff type with critical exponents ⋮ Ground states for critical fractional Schrödinger‐Poisson systems with vanishing potentials ⋮ A class of asymptotically periodic fractional Schrödinger equations with critical growth ⋮ Multiplicity and concentration of nontrivial solutions for fractional Schrödinger-Poisson system involving critical growth ⋮ On critical Schrödinger-Kirchhoff-type problems involving the fractional \(p\)-Laplacian with potential vanishing at infinity ⋮ Ground state and sign-changing solutions for fractional Schrödinger–Poisson system with critical growth ⋮ Ground states for fractional Schrödinger equations with critical growth ⋮ Compact Sobolev-Slobodeckij embeddings and positive solutions to fractional Laplacian equations ⋮ Existence and concentration result for the fractional Schrödinger equations with critical nonlinearities ⋮ Positive ground state solutions for quasicritical the fractional Klein–Gordon–Maxwell system with potential vanishing at infinity ⋮ Solutions of the fractional Schrödinger equation with a sign-changing nonlinearity ⋮ Existence of positive solutions for a class of critical fractional Schrödinger-Poisson system with potential vanishing at infinity ⋮ The fractional Schrödinger equation with Hardy-type potentials and sign-changing nonlinearities ⋮ Multiplicity results for a fractional Schrödinger equation with potentials ⋮ Ground state solutions for a class of fractional Schrödinger-Poisson system with critical growth and vanishing potentials ⋮ Nonautonomous fractional problems with exponential growth ⋮ Existence and multiplicity of solutions for a class of fractional elliptic systems ⋮ Existence and multiplicity of positive solutions to fractional Laplacian systems with combined critical Sobolev terms ⋮ Existence of ground state solutions to Hamiltonian elliptic system with potentials ⋮ Nonlocal Kirchhoff problems with Trudinger -- Moser critical nonlinearities ⋮ Existence and concentration of ground states of fractional nonlinear Schrödinger equations with potentials vanishing at infinity ⋮ Nonlinear perturbations of a periodic fractional Laplacian with supercritical growth ⋮ On a class of fractional Schrödinger equations in with sign-changing potential ⋮ Ground state solutions for fractional Schrödinger equations with critical Sobolev exponent

Cites Work

• Unnamed Item
• Hitchhiker's guide to the fractional Sobolev spaces
• Nonlinear scalar field equations. I: Existence of a ground state
• Existence of minimal nodal solutions for the nonlinear Schrödinger equations with \(V (\infty) = 0\)
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• Best constant in Sobolev inequality
• Nonexistence results for a class of fractional elliptic boundary value problems
• Best constants for Sobolev inequalities for higher order fractional derivatives
• Dual variational methods in critical point theory and applications
• On a fractional Nirenberg problem. I: Blow up analysis and compactness of solutions
• Existence of Solutions for the Nonlinear Schrödinger Equation with V (∞) = 0
• Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity

This page was built for publication: Critical and subcritical fractional problems with vanishing potentials