Concentration-compactness for singular nonlocal Schrödinger equations with oscillatory nonlinearities

DOI10.12775/TMNA.2018.005zbMath1415.35135OpenAlexW2883819831MaRDI QIDQ1741779

Diego Ferraz, João Marcos Bezerra do Ó

Publication date: 7 May 2019

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.tmna/1532484291

zbMATH Keywords

critical Sobolev exponentsfractional Schrödinger equationconcentration-conpactness principle

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Singular elliptic equations (35J75) Fractional partial differential equations (35R11)

Related Items (1)

Ground states for fractional linear coupled systems via profile decomposition ^*

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On interpolation of cocompact imbeddings
• Solutions of Schrödinger equations with inverse square potential and critical nonlinearity
• Hitchhiker's guide to the fractional Sobolev spaces
• Qualitative properties of positive solutions to nonlocal critical problems involving the Hardy-Leray potential
• Concentration-compactness principle for nonlocal scalar field equations with critical growth
• Concentration compactness at the mountain pass level in semilinear elliptic problems
• The Pohozaev identity for the fractional Laplacian
• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms
• Concentrating standing waves for the fractional Schrödinger equation with critical nonlinearities
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Quasilinear asymptotically periodic elliptic equations with critical growth
• Schrödinger equations with critical nonlinearity, singular potential and a ground state
• Positive solutions of elliptic equations with a critical oscillatory nonlinearity
• Sharp constants in the Hardy-Rellich inequalities
• On a class of nonlinear Schrödinger equations
• Existence and multiplicity of solutions of semilinear elliptic equations in \(\mathbb{R}^N\)
• A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space
• On positive entire solutions to a class of equations with a singular coefficient and critical exponent
• Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
• On a fractional Nirenberg problem. I: Blow up analysis and compactness of solutions
• On a class quasilinear Schrödinger equations in ℝⁿ
• 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
• Existence and multiplicity of solutions for superlinear fractional Schrödinger equations in ℝN
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Schrödinger equations with asymptotically periodic terms
• Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.
• Description of the lack of compactness for the Sobolev imbedding
• Characterization of traces of the weighted Sobolev space $W^{1,p}(\Omega,d_M^\epsilon)$ on $M$
• On a class of semilinear elliptic problems in ℝN with critical growth
• Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities
• Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity
• Asymptotically linear fractional Schrödinger equations
• Ground States of some Fractional Schrödinger Equations on ℝ^N
• Existence of Blowing-up Solutions for a Nonlinear Elliptic Equation with Hardy Potential and Critical Growth
• Elliptic Equations with Multi-Singular Inverse-Square Potentials and Critical Nonlinearity
• Ground state solutions for nonlinear fractional Schrödinger equations in $\mathbb {R}^N$RN
• Ground states for fractional Schrödinger equations with critical growth
• On fractional Schr$\ddot{\mbox{o}}$ödinger equation in $\mathbb {R}^{N}$RN with critical growth
• Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations
• An Extension Problem Related to the Fractional Laplacian
• Monotonicity and nonexistence results for some fractional elliptic problems in the half-space
• Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity

This page was built for publication: Concentration-compactness for singular nonlocal Schrödinger equations with oscillatory nonlinearities