On the structure of the nodal set and asymptotics of least energy sign-changing radial solutions of the fractional Brezis-Nirenberg problem

DOI10.1016/j.na.2018.07.001zbMath1401.35094arXiv1708.06149OpenAlexW2964257062WikidataQ129457448 ScholiaQ129457448MaRDI QIDQ1791731

Alessandro Iacopetti, Gabriele Cora

Publication date: 11 October 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.06149

zbMATH Keywords

asymptotic behaviorsign-changing solutionsfractional semilinear elliptic equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11)

Related Items

On the existence of multiple solutions for fractional Brezis–Nirenberg‐type equations ⋮ Existence of sign-changing solution for a problem involving the fractional Laplacian with critical growth nonlinearities

Cites Work

• Unnamed Item
• Unnamed Item
• Non-critical dimensions for critical problems involving fractional Laplacians
• Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
• Hitchhiker's guide to the fractional Sobolev spaces
• A direct method of moving planes for the fractional Laplacian
• The Pohozaev identity for the fractional Laplacian
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Blow-up and symmetry of sign-changing solutions to some critical elliptic equations
• On the classification of solutions of the Lane-Emden equation on unbounded domains of \(\mathbb R^N\)
• Stability of variational eigenvalues for the fractional \(p\)-Laplacian
• Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem
• Bifurcation and multiplicity results for critical nonlocal fractional Laplacian problems
• Proof of two conjectures of H. Brezis and L. A. Peletier
• On the Brézis-Nirenberg problem
• An existence result for nonliner elliptic problems involving critical Sobolev exponent
• Variational and topological methods in partially ordered Hilbert spaces
• Comparison results and steady states for the Fujita equation with fractional Laplacian.
• Some existence results for superlinear elliptic boundary value problems involving critical exponents
• Best constants for Sobolev inequalities for higher order fractional derivatives
• A Brezis-Nirenberg result for non-local critical equations in low dimension
• Uniqueness and nondegeneracy of positive solutions of \((-\Delta )^su+u= u^p\) in \(\mathbb R^N\) when s is close to 1
• \(H^s\) versus \(C^0\)-weighted minimizers
• A non-existence result for low energy sign-changing solutions of the Brezis-Nirenberg problem in dimensions 4, 5 and 6
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• Multiple solutions for the Brezis-Nirenberg problem
• Blow-up and nonexistence of sign changing solutions to the Brezis-Nirenberg problem in dimension three
• Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian
• Uniqueness of Radial Solutions for the Fractional Laplacian
• The Yamabe equation in a non-local setting
• Geometria Differenziale
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Elementary proof of the nonexistence of nodal solutions for the semilinear elliptic equations with critical sobolev exponent
• Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
• The Poincare-Miranda Theorem
• Sign-changing blowing-up solutions for the Brezis-Nirenberg problem in dimensions four and five
• SOBOLEV INEQUALITIES WITH SYMMETRY
• Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations
• An Extension Problem Related to the Fractional Laplacian
• Variational Methods
• The Brezis-Nirenberg result for the fractional Laplacian
• Sign-changing tower of bubbles for the Brezis–Nirenberg problem

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