Existence and concentration result for the fractional Schrödinger equations with critical nonlinearities
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Publication:502244
DOI10.1007/s00526-016-1045-0zbMath1395.35193OpenAlexW2463232867MaRDI QIDQ502244
Publication date: 3 January 2017
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00526-016-1045-0
Smoothness and regularity of solutions to PDEs (35B65) Variational methods for elliptic systems (35J50) Fractional partial differential equations (35R11)
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Cites Work
- Unnamed Item
- On some critical problems for the fractional Laplacian operator
- Hitchhiker's guide to the fractional Sobolev spaces
- Concentration phenomenon for fractional nonlinear Schrödinger equations
- A critical fractional equation with concave-convex power nonlinearities
- The Brezis-Nirenberg type problem involving the square root of the Laplacian
- Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
- 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
- Positive solutions of nonlinear problems involving the square root of the Laplacian
- On a class of nonlinear Schrödinger equations
- Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology
- Fractional quantum mechanics and Lévy path integrals
- Elliptic partial differential equations of second order
- On the variational principle
- Best constants for Sobolev inequalities for higher order fractional derivatives
- Local mountain passes for semilinear elliptic problems in unbounded domains
- Minimax theorems
- A Brezis-Nirenberg result for non-local critical equations in low dimension
- Dual variational methods in critical point theory and applications
- Concentrating standing waves for the fractional nonlinear Schrödinger equation
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- On a fractional Nirenberg problem. I: Blow up analysis and compactness of solutions
- Critical and subcritical fractional problems with vanishing potentials
- A concave—convex elliptic problem involving the fractional Laplacian
- Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
- Fractional Elliptic Problems with Critical Growth in the Whole of ℝn
- A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
- Multiple Solutions for a Nonlinear Schrödinger Equation with Magnetic Fields
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
- Multiplicity of Positive Solutions For a Quasilinear Problem in IRN Via Penalization Method
- Regularity of the obstacle problem for a fractional power of the laplace operator
- A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
- Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity
- Multiple semiclassical standing waves for fractional nonlinear Schrödinger equations
- 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
- Multiplicity and concentration behavior of positive solutions for a Schrödinger–Kirchhoff type problemviapenalization method
- An Extension Problem Related to the Fractional Laplacian
- Classification of solutions for an integral equation
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