Concentration phenomenon for a fractional Schrödinger equation with discontinuous nonlinearity

DOI10.3934/dcdss.2023074OpenAlexW4362653886MaRDI QIDQ6189920

Vincenzo Ambrosio

Publication date: 5 February 2024

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2023074

zbMATH Keywords

nonsmooth analysispenalization methodfractional operatorsdiscontinuous nonlinearityconcentration phenomenon

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Schrödinger operator, Schrödinger equation (35J10) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11)

Related Items (1)

An existence result for a fractional critical \((p, q)\)-Laplacian problem with discontinuous nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• Hitchhiker's guide to the fractional Sobolev spaces
• Existence of solutions for an NSE with discontinuous nonlinearity
• Existence and multiplicity of solutions for fractional elliptic problems with discontinuous nonlinearities
• Variational methods for non-differentiable functionals and their applications to partial differential equations
• On a class of nonlinear Schrödinger equations
• The dual variational principle and elliptic problems with discontinuous nonlinearities
• Mountain pass theorems for non-differentiable functions and applications
• Some discontinuous problems with a quasilinear operator
• Multiplicity of positive solutions for a class of fractional Schrödinger equations via penalization method
• A critical fractional \(p\)-Kirchhoff type problem involving discontinuous nonlinearity
• On concentration of positive bound states of nonlinear Schrödinger equations
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Minimax theorems
• Existence and behavior of the solutions for an elliptic equation with a nonlocal operator involving critical and discontinuous nonlinearity
• Concentrating solutions for a class of nonlinear fractional Schrödinger equations in \(\mathbb{R}^N\)
• Concentrating standing waves for the fractional nonlinear Schrödinger equation
• On existence and concentration of solutions for an elliptic problem with discontinuous nonlinearity via penalization method
• Existence and concentration of solution for a class of fractional elliptic equation in \(\mathbb {R}^N\) via penalization method
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• Nonlinear Diffusion with Fractional Laplacian Operators
• Variational Methods for Nonlocal Fractional Problems
• Optimization and nonsmooth analysis
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• Generalized Gradients and Applications
• Existence and multiplicity results for elliptic problems with critical growth and discontinuous nonlinearities
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• The weak upper and lower solution method for quasilinear elliptic equations with generalized subdifferentiable perturbations
• Existence and Concentration of Solutions for a Class of Elliptic Problems with Discontinuous Nonlinearity in $\mathbf{R}^{N}$
• Nonlinear Fractional Schrödinger Equations in R^N
• Existence of positive solution for Kirchhoff type problem with critical discontinuous nonlinearity
• An introduction to minimax theorems and their applications to differential equations
• A nonsmooth critical point theory approach to some nonlinear elliptic equations in \({\mathbb R}^n\)
• A variational approach to discontinuous problems with critical Sobolev exponents

This page was built for publication: Concentration phenomenon for a fractional Schrödinger equation with discontinuous nonlinearity