Existence of solutions for a fractional Choquard-type equation in \(\mathbb{R}\) with critical exponential growth

DOI10.1007/s00033-020-01447-wzbMath1466.35175arXiv2007.00773OpenAlexW3120108961WikidataQ115609381 ScholiaQ115609381MaRDI QIDQ2026440

Rodrigo Clemente, Eudes Barboza, José Carlos de Albuquerque

Publication date: 19 May 2021

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.00773

zbMATH Keywords

existence of solutionsvariational methodscritical exponential growthfractional Choquard-type equations

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Critical exponents in context of PDEs (35B33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11)

Related Items (9)

Existence of ground state solutions for critical fractional Choquard equations involving periodic magnetic field ⋮ On nonlinear perturbations of a periodic integrodifferential Kirchhoff equation with critical exponential growth ⋮ On some qualitative aspects for doubly nonlocal equations ⋮ Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case ⋮ One‐dimensional periodic fractional Schrödinger equations with exponential critical growth ⋮ Existence of solution for a class of fractional Hamiltonian-type elliptic systems with exponential critical growth in R ⋮ Multiplicity and concentration of solutions to a fractional \((p,p_1)\)-Laplace problem with exponential growth ⋮ Semiclassical states of fractional Choquard equations with exponential critical growth ⋮ Global attractors of the degenerate fractional Kirchhoff wave equation with structural damping or strong damping

Cites Work

• Unnamed Item
• Unnamed Item
• A fractional Moser-Trudinger type inequality in one dimension and its critical points.
• Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in \(\mathbb R^2\)
• Hitchhiker's guide to the fractional Sobolev spaces
• A Hopf's lemma and a strong minimum principle for the fractional \(p\)-Laplacian
• Stationary solutions of the Schrödinger-Newton model -- an ODE approach.
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The one-dimensional Schrödinger-Newton equations
• Elliptic equations in \(R^ 2\) with nonlinearities in the critical growth range
• On critical cases of Sobolev's inequalities
• On gravity's role in quantum state reduction
• Ground state solutions for a nonlocal equation in \(\mathbb{R}^2\) involving vanishing potentials and exponential critical growth
• \(n\)-Kirchhoff-Choquard equations with exponential nonlinearity
• Critical and subcritical fractional Trudinger-Moser-type inequalities on \(\mathbb{R}\)
• Multiplicity of solutions for a nonlocal nonhomogeneous elliptic equation with critical exponential growth
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• On nonlinear perturbations of a periodic fractional Schrödinger equation with critical exponential growth
• Critical growth problems for ½-Laplacian in ℝ
• Non-local Diffusions, Drifts and Games
• Semiclassical ground state solutions for a Choquard type equation in ℝ²with critical exponential growth
• Upper bound of the best constant of the Trudinger-Moser inequality and its application to the Gagliardo-Nirenberg inequality
• The Choquard equation and related questions
• Nontrivial Solution of Semilinear Elliptic Equations with Critical Exponent in R
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Existence of solutions for a nonlocal variational problem in $\mathbb{R}^2$ with exponential critical growth
• Multi-peak solutions for nonlinear Choquard equation in the plane
• Existence of groundstates for a class of nonlinear Choquard equations

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