Concentration of solutions for fractional double-phase problems: critical and supercritical cases

DOI10.1016/j.jde.2021.08.038zbMath1481.35385OpenAlexW3196429246MaRDI QIDQ2232181

Vicenţiu D. Rădulescu, Youpei Zhang, Xian Hua Tang

Publication date: 4 October 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2021.08.038

zbMATH Keywords

penalizationcritical problemNehari manifoldsupercritical problemfractional double-phase problemdouble phase energy

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects) (55M30) Singular perturbations in context of PDEs (35B25) Critical exponents in context of PDEs (35B33) Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (9)

Double phase problems with competing potentials: concentration and multiplication of ground states ⋮ Multiplicity and concentration of positive solutions for fractional unbalanced double-phase problems ⋮ Hölder continuity and boundedness estimates for nonlinear fractional equations in the Heisenberg group ⋮ Concentrating solutions for singularly perturbed double phase problems with nonlocal reaction ⋮ A double phase problem with a nonlinear boundary condition ⋮ Multiplicity and concentration of solutions to fractional anisotropic Schrödinger equations with exponential growth ⋮ Quasilinear double phase problems with parameter dependent performance on the whole space ⋮ Multiplicity and concentration properties for \((p,q)\)-Kirchhoff non-autonomous problems with Choquard nonlinearity ⋮ On fractional Musielak-Sobolev spaces and applications to nonlocal problems

Cites Work

• Unnamed Item
• Unnamed Item
• On the electrostatic Born-Infeld equation with extended charges
• Multiple integrals in the calculus of variations
• On the definition and the lower semicontinuity of certain quasiconvex integrals
• Strong comparison principle for the fractional \(p\)-Laplacian and applications to starshaped rings
• Higher integrability for minimizers of integral functionals with \((p,q)\) growth
• On the variational principle
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Minimax theorems
• On existence and concentration behavior of positive ground state solutions for a class of fractional Schrödinger-Choquard equations
• Existence and concentration of positive solutions for a Schrödinger logarithmic equation
• Recent developments in problems with nonstandard growth and nonuniform ellipticity
• Fractional \(p \& q\) Laplacian problems in \(\mathbb{R}^N\) with critical growth
• Fractional double-phase patterns: concentration and multiplicity of solutions
• On the multiplicity and concentration of positive solutions for a \(p\)-fractional Choquard equation in \(\mathbb{R}^N\)
• Dual variational methods in critical point theory and applications
• The concentration behavior of ground states for a class of Kirchhoff-type problems with Hartree-type nonlinearity
• Existence, multiplicity and concentration for a class of fractional \( p \& q \) Laplacian problems in \( \mathbb{R} ^{N} \)
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• A reformulation of the Born-Infeld electrodynamics
• Variational Methods for Nonlocal Fractional Problems
• Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• Foundations of the New Field Theory
• Concentration of positive solutions for a class of fractionalp-Kirchhoff type equations
• Lipschitz Bounds and Nonuniform Ellipticity
• Existence and concentration results for some fractional Schrödinger equations in RN with magnetic fields

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