A critical elliptic problem involving fractional Laplacian operator in domains with shrinking holes

DOI10.1016/j.jde.2019.04.029zbMath1423.35112OpenAlexW2944765404WikidataQ127918227 ScholiaQ127918227MaRDI QIDQ2420543

Wei Long, Shusen Yan, Jianfu Yang

Publication date: 6 June 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2019.04.029

zbMATH Keywords

critical exponentblow upfractional Laplaciansemilinear nonlocal equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Critical exponents in context of PDEs (35B33) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11)

Related Items

Sign-changing bubble tower solutions for a critical fractional problem, Existence and regularity of solutions for a class of fractional Laplacian problems, On the fractional Lazer-McKenna conjecture with critical growth, Coron's problem for the critical Lane-Emden system, Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods, The fractional Brezis-Nirenberg problems on lower dimensions, The existence of constrained minimizers related to fractional \(p\)-Laplacian equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains
• On some critical problems for the fractional Laplacian operator
• Hitchhiker's guide to the fractional Sobolev spaces
• Bubbling solutions for nonlocal elliptic problems
• The Brezis-Nirenberg type problem involving the square root of the Laplacian
• Infinitely many positive solutions for an elliptic problem with critical or supercritical growth
• Mountain pass solutions for non-local elliptic operators
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Infinitely many solutions for the prescribed scalar curvature problem on \(\mathbb S^N\)
• An elliptic problem with critical growth in domains with shrinking holes.
• Concentration of solutions for the scalar curvature equation on \(\mathbb{R}^n\)
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• Positive solutions for non local elliptic problems
• Variational methods for non-local operators of elliptic type
• A Brezis-Nirenberg result for non-local critical equations in low dimension
• Equations involving fractional Laplacian operator: compactness and application
• Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian
• Nondegeneracy of the bubble in the critical case for nonlocal equations
• Multiple solutions to the Bahri-Coron problem in some domains with nontrivial topology
• A concave—convex elliptic problem involving the fractional Laplacian
• Existence and symmetry results for a Schr\"odinger type problem involving the fractional Laplacian
• A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality
• Little holes and convergence of solutions of −Δu = u(N + 2)⧸(N - 2)
• Lévy Processes and Stochastic Calculus
• Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains
• An Extension Problem Related to the Fractional Laplacian
• Classification of solutions for an integral equation
• Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality