Fractional \(p \& q\) Laplacian problems in \(\mathbb{R}^N\) with critical growth

DOI10.4171/ZAA/1661zbMath1446.35245arXiv1801.10449MaRDI QIDQ2197921

Vincenzo Ambrosio

Publication date: 1 September 2020

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.10449

zbMATH Keywords

concentration-compactness lemmaexistence of a nontrivial non-negative solution

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Critical exponents in context of PDEs (35B33) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Fractional partial differential equations (35R11)

Related Items (33)

Existence results for a Kirchhoff-type equations involving the fractional \(p_1(x)\) \& \(p_2(x)\)-Laplace operator ⋮ Global existence and asymptotic behavior of solutions to fractional ( p , q )-Laplacian equations ⋮ Infinitely many solutions for a doubly nonlocal fractional problem involving two critical nonlinearities ⋮ Discrete Picone inequalities and applications to non local and non homogenenous operators ⋮ Ground states for Schrödinger-Kirchhoff equations of fractional \(p\)-Laplacian involving logarithmic and critical nonlinearity ⋮ Existence of solutions for the fractional \((p, q)\)-Laplacian problems involving a critical Sobolev exponent ⋮ Multiplicity and concentration of positive solutions for fractional unbalanced double-phase problems ⋮ Existence and multiplicity for fractional \(p\)-Kirchhoff problem with competitive nonlinearities and critical growth ⋮ Positive solutions for singular anisotropic \((p, q)\)-equations ⋮ Fractional \((p, q)\)-Schrödinger equations with critical and supercritical growth ⋮ Multiplicity and concentration of solutions for a fractional \(p\)-Kirchhoff type equation ⋮ An existence result for a fractional critical \((p, q)\)-Laplacian problem with discontinuous nonlinearity ⋮ The concentration-compactness principle for the nonlocal anisotropic \(p\)-Laplacian of mixed order ⋮ An existence result for a fractional elliptic system involving (p,q)-Laplacian and critical exponent ⋮ Multiple solutions of \(p\)-fractional Schrödinger-Choquard-Kirchhoff equations with Hardy-Littlewood-Sobolev critical exponents ⋮ Critical fractional \((p, q)\)-Kirchhoff type problem with a generalized Choquard nonlinearity and magnetic field ⋮ Existence of least energy sign-changing solution for a class of fractional p & q -Laplacian problems with potentials vanishing at infinity ⋮ Fractional double-phase patterns: concentration and multiplicity of solutions ⋮ Regularity and multiplicity results for fractional (p,q)-Laplacian equations ⋮ Degenerate Kirchhoff \((p, q)\)-fractional systems with critical nonlinearities ⋮ Concentration of solutions for fractional double-phase problems: critical and supercritical cases ⋮ Existence and concentration of positive solutions for a critical \(p\)\&\(q\) equation ⋮ Existence for \((p, q)\) critical systems in the Heisenberg group ⋮ Multiplicity of positive solutions for a fractional \(p\& q\)-Laplacian problem in \(\mathbb{R}^N\) ⋮ Unnamed Item ⋮ Existence for fractional \((p,q)\) systems with critical and Hardy terms in \(\mathbb{R}^N\) ⋮ Multiplicity of weak positive solutions for fractional \(p\& q\) Laplacian problem with singular nonlinearity ⋮ Global regularity results for non-homogeneous growth fractional problems ⋮ A strong maximum principle for the fractional \(( p , q )\)-Laplacian operator ⋮ Existence of solutions for critical fractional p&q-Laplacian system ⋮ On fractional \((p, q)\)-Laplacian equations involving subcritical or critical Hardy exponents ⋮ Nodal solutions for double phase Kirchhoff problems with vanishing potentials ⋮ A Kirchhoff type equation in \(\mathbb{R}^N\) Involving the fractional \((p, q)\)-Laplacian

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