Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method

DOI10.1515/fca-2020-0042zbMath1474.35641OpenAlexW3042444417MaRDI QIDQ2209181

Amani Hammami, Adel Daoues, Kamel Saoudi

Publication date: 28 October 2020

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

Full work available at URL: https://doi.org/10.1515/fca-2020-0042

zbMATH Keywords

multiple positive solutionssingular nonlinearitynonlocal operatorHardy-Sobolev exponentvariational and approximation methods

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)

Related Items (7)

Nonlocal p-Kirchhoff equations with singular and critical nonlinearity terms ⋮ Unnamed Item ⋮ Existence and multiplicity of solutions for a nonlocal problem with critical Sobolev-Hardy nonlinearities ⋮ Existence and Hölder regularity of infinitely many solutions to a \(p\)-Kirchhoff-type problem involving a singular nonlinearity without the Ambrosetti-Rabinowitz (AR) condition ⋮ A critical fractional Choquard problem involving a singular nonlinearity and a Radon measure ⋮ Existence and multiple of solutions for a class integro-differential equations with singular term via variational and Galerkin methods ⋮ Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable

Cites Work

• On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations
• A free fractional viscous oscillator as a forced standard damped vibration
• Semilinear problems for the fractional Laplacian with a singular nonlinearity
• Hitchhiker's guide to the fractional Sobolev spaces
• Convexity properties of Dirichlet integrals and Picone-type inequalities
• A critical fractional equation with concave-convex power nonlinearities
• Mountain pass solutions for non-local elliptic operators
• A general mountain pass principle for locating and classifying critical points
• A critical fractional elliptic equation with singular nonlinearities
• Nonlocal problems with critical Hardy nonlinearity
• Variational methods for non-local operators of elliptic type
• A Brezis-Nirenberg result for non-local critical equations in low dimension
• Existence and multiplicity of solutions for nonlinear elliptic problems with the fractional Laplacian
• Critical growth fractional elliptic problem with singular nonlinearities
• From the long jump random walk to the fractional Laplacian
• Variational Methods for Nonlocal Fractional Problems
• The Nehari manifold for a singular elliptic equation involving the fractional Laplace operator
• Financial Modelling with Jump Processes
• Multiplicity and Hölder regularity of solutions for a nonlocal elliptic PDE involving singularity
• An Extension Problem Related to the Fractional Laplacian
• A multiplicity results for a singular problem involving the fractionalp-Laplacian operator
• Bernstein functions. Theory and applications

This page was built for publication: Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method