Multi-peak solutions of a class of fractional \(p\)-Laplacian equations

DOI10.1007/s12220-023-01475-8OpenAlexW4388946482MaRDI QIDQ6143869

Yohei Sato, Xiaojun Chang, Chengxiang Zhang

Publication date: 5 January 2024

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-023-01475-8

zbMATH Keywords

variational methodsmulti-peak solutionspenalization techniquefractional \(p\)-Laplacian equations

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Variational methods applied to PDEs (35A15) Integro-differential operators (47G20) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multi-peak positive solutions for a fractional nonlinear elliptic equation
• Optimal decay of extremals for the fractional Sobolev inequality
• Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential
• Non-local gradient dependent operators
• Hitchhiker's guide to the fractional Sobolev spaces
• Existence and concentration result for the fractional Schrödinger equations with critical nonlinearities
• The Brezis-Nirenberg problem for the fractional \(p\)-Laplacian
• Global Hölder regularity for the fractional \(p\)-Laplacian
• Asymptotically linear fractional \(p\)-Laplacian equations
• A Hopf's lemma and a strong minimum principle for the fractional \(p\)-Laplacian
• Nonlinear scalar field equations. I: Existence of a ground state
• Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results
• Standing waves with a critical frequency for nonlinear Schrödinger equations. II.
• Fractional quantum mechanics and Lévy path integrals
• Maximum principles for the fractional p-Laplacian and symmetry of solutions
• Remarks about a fractional Choquard equation: ground state, regularity and polynomial decay
• Bifurcation results for problems with fractional Trudinger-Moser nonlinearity
• Entire solutions for critical \(p\)-fractional Hardy Schrödinger Kirchhoff equations
• Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional \(p\)-Laplacian
• Monotonicity of positive solutions for nonlocal problems in unbounded domains
• Spectrum of the fractional \(p\)-Laplacian in \(\mathbb{R}^N\) and decay estimate for positive solutions of a Schrödinger equation
• Standing waves for the pseudo-relativistic Hartree equation with Berestycki-Lions nonlinearity
• Nodal multi-peak standing waves of fourth-order Schrödinger equations with mixed dispersion
• A multiplicity result for a \((p,q)\)-Schrödinger-Kirchhoff type equation
• Multi-peak semiclassical bound states for fractional Schrödinger equations with fast decaying potentials
• Fractional double-phase patterns: concentration and multiplicity of solutions
• Existence of single peak solutions for a nonlinear Schrödinger system with coupled quadratic nonlinearity
• Concentrating solutions of nonlinear fractional Schrödinger equation with potentials
• Semi-classical states for the nonlinear Choquard equations: existence, multiplicity and concentration at a potential well
• Existence and concentration of positive solutions for \(p\)-fractional Schrödinger equations
• Remarks on a nonlinear nonlocal operator in Orlicz spaces
• Concentrating standing waves for the fractional nonlinear Schrödinger equation
• Existence, multiplicity and concentration for a class of fractional \( p \& q \) Laplacian problems in \( \mathbb{R} ^{N} \)
• Multi-peak standing waves for nonlinear Schrödinger equations with a general nonlinearity
• Existence and concentration of solution for a class of fractional elliptic equation in \(\mathbb {R}^N\) via penalization method
• Sign-changing solutions of fractional $p$-Laplacian problems
• Standing waves for nonlinear Schrödinger equations with a general nonlinearity
• Existence of a positive solution for some quasilinear elliptic equations in \(\mathbb{R}^N\)
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• Non-local Diffusions, Drifts and Games
• A Nonlocalp-Laplacian Evolution Equation with Nonhomogeneous Dirichlet Boundary Conditions
• Standing Waves for Nonlinear Schrodinger Equations with a General Nonlinearity: One and Two Dimensional Cases
• Symmetric Decreasing Rearrangement Is Sometimes Continuous
• On the Ambrosetti-Rabinowitz Superlinear Condition
• Existence and Concentration of Bound States for a p-Laplacian Equation in ℝ^N
• Monotonicity and symmetry of positive solutions to fractional p-Laplacian equation
• Fractional p-eigenvalues
• Nonlinear scalar field equations involving the fractional Laplacian
• An Extension Problem Related to the Fractional Laplacian
• Monotonicity of eigenvalues of the fractional \(p\)-Laplacian with singular weights

This page was built for publication: Multi-peak solutions of a class of fractional \(p\)-Laplacian equations