Fractional Kirchhoff problems with critical Trudinger-Moser nonlinearity

DOI10.1007/s00526-019-1499-yzbMath1407.35216OpenAlexW2916461675MaRDI QIDQ667535

Vicenţiu D. Rădulescu, Binlin Zhang, Mingqi Xiang

Publication date: 28 February 2019

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-019-1499-y

zbMATH Keywords

critical Trudinger-Moser nonlinearityfractional Kirchhoff problems

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Integro-differential operators (47G20) Fractional partial differential equations (35R11)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Critical stationary Kirchhoff equations in \(\mathbb R^N\) involving nonlocal operators
• Ground state solution for a Kirchhoff problem with exponential critical growth
• Existence theorems for entire solutions of stationary Kirchhoff fractional \(p\)-Laplacian equations
• Hitchhiker's guide to the fractional Sobolev spaces
• Existence of solutions for Kirchhoff type problem involving the non-local fractional \(p\)-Laplacian
• Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity
• On a class of nonhomogeneous fractional quasilinear equations in \(\mathbb R^n\) with exponential growth
• Fractional Adams-Moser-Trudinger type inequalities
• Nonlocal Schrödinger-Kirchhoff equations with external magnetic field
• Multiplicity of solutions for \(p(x)\)-polyharmonic elliptic Kirchhoff equations
• Existence and multiplicity of solutions to equations of \(N\)-Laplacian type with critical exponential growth in \(\mathbb R^N\)
• A global multiplicity result for \(N\)-Laplacian with critical nonlinearity of concave-convex type
• Multiple solutions for nonhomogeneous Schrödinger-Kirchhoff type equations involving the fractional \(p\)-Laplacian in \(\mathbb R^N\)
• Ground state solutions of scalar field fractional Schrödinger equations
• On a quasilinear nonhomogeneous elliptic equation with critical growth in \(\mathbb R^N\)
• Global solvability for the degenerate Kirchhoff equation with real analytic data
• Elliptic equations in \(R^ 2\) with nonlinearities in the critical growth range
• Fractional quantum mechanics and Lévy path integrals
• Bifurcation results for problems with fractional Trudinger-Moser nonlinearity
• Existence of solutions for a critical fractional Kirchhoff type problem in \(\mathbb{R}^N\)
• On critical cases of Sobolev's inequalities
• Multiple solutions for \(N\)-Kirchhoff type problems with critical exponential growth in \(\mathbb{R}^N\)
• \(1/2\)-Laplacian problems with exponential nonlinearity
• A nonhomogeneous fractional \(p\)-Kirchhoff type problem involving critical exponent in \(\mathbb{R}^N\)
• Existence and multiplicity of entire solutions for fractional \(p\)-Kirchhoff equations
• Fractional elliptic equations with critical exponential nonlinearity
• A critical Kirchhoff type problem involving a nonlocal operator
• Infinitely many solutions for the stationary Kirchhoff problems involving the fractionalp-Laplacian
• Non-local Diffusions, Drifts and Games
• Nonlocal Kirchhoff diffusion problems: local existence and blow-up of solutions
• Degenerate Kirchhoff problems involving the fractionalp-Laplacian without the (AR) condition
• Upper bound of the best constant of the Trudinger-Moser inequality and its application to the Gagliardo-Nirenberg inequality
• Variational Methods for Nonlocal Fractional Problems
• An Extension Problem Related to the Fractional Laplacian
• Multiple solutions for a class of fractional quasi-linear equations with critical exponential growth in ℝ^N
• On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces

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