Critical fractional \(p\)-Laplacian problems with possibly vanishing potentials

DOI10.1016/j.jmaa.2015.08.024zbMath1403.35319arXiv1504.01533OpenAlexW1703060281MaRDI QIDQ499168

Marco Squassina, Perera, Kanishka, Yingchen Yang

Publication date: 30 September 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.01533

zbMATH Keywords

critical exponentnontrivial solutionsfractional \(p\)-Laplacian\(\mathbb{Z}_2\)-cohomological indexexternal potentialsgeneralized linking

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (14)

Multiple solutions for fractional \(p\)-Laplace equation with concave-convex nonlinearities ⋮ Unnamed Item ⋮ Fractional Schrödinger equations involving potential vanishing at infinity and supercritical exponents ⋮ EXISTENCE OF WEAK SOLUTIONS TO A CLASS OF SCHRODINGER TYPE EQUATIONS INVOLVING THE FRACTIONAL p-LAPLACIAN IN R-N ⋮ The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis-Nirenberg problem ⋮ The Nehari manifold for a fractional $p$-Kirchhoff system involving sign-changing weight function and concave-convex nonlinearities ⋮ Ground state solution for asymptotically periodic fractional \(p\)-Laplacian equation ⋮ Existence of multiple solutions for fractional \(p\)-Kirchhoff equations with concave-convex nonlinearities ⋮ Multiplicity of solutions for a class of fractional Choquard-Kirchhoff equations involving critical nonlinearity ⋮ The Nehari manifold for fractional \(p\)-Laplacian equation with logarithmic nonlinearity on whole space ⋮ Global existence and blow-up for the fractional \(p\)-Laplacian with logarithmic nonlinearity ⋮ Existence of positive solutions for a class of critical fractional Schrödinger-Poisson system with potential vanishing at infinity ⋮ Multiplicity results for a fractional Schrödinger equation with potentials ⋮ The Nehari manifold for a class of Schrödinger equation involving fractional p-Laplacian and sign-changing logarithmic nonlinearity

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