Existence, nonexistence, and multiplicity of solutions for the fractional \(p\&q\)-Laplacian equation in \(\mathbb R^N\)

DOI10.1186/S13661-016-0661-0zbMath1344.35161OpenAlexW2512519295WikidataQ59466611 ScholiaQ59466611MaRDI QIDQ308548

Jinfeng Bao, Caisheng Chen

Publication date: 6 September 2016

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-016-0661-0

zbMATH Keywords

variational methods\((PS)_c\) conditionfractional \(p\&q\)-Laplacian equation

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Nonlinear elliptic equations (35J60) Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (19)

Existence of a mountain pass solution for a nonlocal fractional \((p, q)\)-Laplacian problem ⋮ Existence results for a Kirchhoff-type equations involving the fractional \(p_1(x)\) \& \(p_2(x)\)-Laplace operator ⋮ Fractional double phase Robin problem involving variable order-exponents without Ambrosetti-Rabinowitz condition ⋮ Existence of solutions for the fractional \((p, q)\)-Laplacian problems involving a critical Sobolev exponent ⋮ Existence, multiplicity and concentration for a class of fractional \( p \& q \) Laplacian problems in \( \mathbb{R} ^{N} \) ⋮ Existence of solutions for fractional p&q-Laplacian system involving critical sandwich-type nonlinearities ⋮ Fractional p&q-Laplacian problems with potentials vanishing at infinity ⋮ Fractional \(p \& q\) Laplacian problems in \(\mathbb{R}^N\) with critical growth ⋮ Critical fractional \((p, q)\)-Kirchhoff type problem with a generalized Choquard nonlinearity and magnetic field ⋮ Fractional double-phase patterns: concentration and multiplicity of solutions ⋮ Regularity and multiplicity results for fractional (p,q)-Laplacian equations ⋮ On a fractional \(p \& q\) Laplacian problem with critical Sobolev-Hardy exponents ⋮ Multiplicity of solutions for fractional \(p\& q\)-Laplacian system involving critical concave-convex nonlinearities ⋮ Multiplicity of positive solutions for a fractional \(p\& q\)-Laplacian problem in \(\mathbb{R}^N\) ⋮ Multiplicity of weak positive solutions for fractional \(p\& q\) Laplacian problem with singular nonlinearity ⋮ Unnamed Item ⋮ Existence of solutions for critical fractional p&q-Laplacian system ⋮ 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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