Existence and multiplicity of solutions for nonlinear elliptic problems with the fractional Laplacian

DOI10.1515/fca-2015-0009zbMath1323.35204OpenAlexW2562639299MaRDI QIDQ2260538

Qing-Mei Zhou, Ke-Qi Wang

Publication date: 11 March 2015

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/fca-2015-0009

zbMATH Keywords

Dirichlet problemfractional Sobolev spacesthree critical points theoremfractional Laplacian

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Fractional derivatives and integrals (26A33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11)

Related Items (12)

Sign-changing solutions for a class of fractional Kirchhoff-type problem with logarithmic nonlinearity ⋮ No local \(L^{1}\) solutions for semilinear fractional heat equations ⋮ Lyapunov-type inequalities for a fractional \(p\)-Laplacian system ⋮ A critical fractional elliptic equation with singular nonlinearities ⋮ On an eigenvalue problem involving the fractional \((s, p)\)-Laplacian ⋮ Infinitely many solutions of nonlocal Kirchhoff-type equations via perturbation methods ⋮ Infinitely many sign-changing solutions for the Brézis-Nirenberg problem involving the fractional Laplacian ⋮ Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method ⋮ Asymptotical dynamics for non-autonomous stochastic equations driven by a non-local integro-differential operator of fractional type ⋮ Existence and multiplicity of solutions for a nonlocal problem with critical Sobolev-Hardy nonlinearities ⋮ Positive solutions to nonlinear systems involving fully nonlinear fractional operators ⋮ Nonlinear fractional equations with supercritical growth

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