A critical nonlinear fractional elliptic equation with saddle-like potential in ℝN

DOI10.1063/1.4959221zbMath1346.35205arXiv1506.06533OpenAlexW2506796672MaRDI QIDQ2820866

Olímpio Hiroshi Miyagaki, Claudianor Oliveira Alves

Publication date: 12 September 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.06533

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Fractional partial differential equations (35R11)

Related Items (6)

A multiplicity result for a nonlinear fractional Schrödinger equation in \(\mathbb{R}^N\) without the Ambrosetti-Rabinowitz condition ⋮ The critical fractional Schrödinger equation with a small superlinear term ⋮ Existence of a positive solution for a logarithmic Schrödinger equation with saddle-like potential ⋮ Ground state of Kirchhoff type fractional Schrödinger equations with critical growth ⋮ Global bifurcation results for a fractional equation in \(\mathbb{R}^N\) ⋮ Nonlocal Schrödinger equations for integro-differential operators with measurable kernels

Cites Work

• Existence of a positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in \({\mathbb{R}^{2}}\)
• Hitchhiker's guide to the fractional Sobolev spaces
• Concentration phenomenon for fractional nonlinear Schrödinger equations
• Existence of positive solutions of the equation \(-\Delta u+a(x)u=u^{(N+2)/(N-2)}\) in \({\mathbb{R}}^ N\)
• On a class of nonlinear Schrödinger equations
• On concentration of positive bound states of nonlinear Schrödinger equations
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• On existence and concentration behavior of ground state solutions for a class of problems with critical growth.
• Best constants for Sobolev inequalities for higher order fractional derivatives
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Concentrating solutions of nonlinear fractional Schrödinger equation with potentials
• Concentrating standing waves for the fractional nonlinear Schrödinger equation
• Nodal and multiple solutions of nonlinear problems involving the fractional Laplacian
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• Uniqueness of Radial Solutions for the Fractional Laplacian
• A concave—convex elliptic problem involving the fractional Laplacian
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• Existence and symmetry results for a Schr\"odinger type problem involving the fractional Laplacian
• Multiplicity of Positive Solutions For a Quasilinear Problem in IR^N Via Penalization Method
• Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)_a
• Existence of positive bound states of nonlinear Schrödinger equations with saddle-like potential
• NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• Ground states and concentration phenomena for the fractional Schrödinger equation
• Ground state solutions for nonlinear fractional Schrödinger equations in $\mathbb {R}^N$RN
• On fractional Schr$\ddot{\mbox{o}}$ödinger equation in $\mathbb {R}^{N}$RN with critical growth
• An Extension Problem Related to the Fractional Laplacian
• Nonlinear perturbations of a periodic elliptic problem with critical growth.
• On a class of nonlinear Schrödinger equations in \(\mathbb R^2\) involving critical growth
• Local mountain-pass for a class of elliptic problems in \(\mathbb R^N\) involving critical growth

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