A fractional elliptic problem in \(\mathbb {R}^n\) with critical growth and convex nonlinearities

DOI10.1007/S00229-018-1032-1zbMath1426.35222arXiv1609.01911OpenAlexW2513324383MaRDI QIDQ1728390

Claudia Bucur, María Medina

Publication date: 22 February 2019

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01911

zbMATH Keywords

mountain pass theoremconcentration-compactness

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Nonlinear elliptic equations (35J60) Weak solutions to PDEs (35D30) Variational methods for second-order elliptic equations (35J20) Fractional partial differential equations (35R11)

Related Items (4)

Unnamed Item ⋮ Asymptotic behavior of ground states and local uniqueness for fractional Schrödinger equations with nearly critical growth ⋮ Effect of the domain geometry on the solutions to fractional Brezis-Nirenberg problem ⋮ Existence and multiplicity of solutions for fractional Laplacian system

Cites Work

• Unnamed Item
• Nonlocal diffusion and applications
• Hitchhiker's guide to the fractional Sobolev spaces
• A critical fractional equation with concave-convex power nonlinearities
• Bifurcation results for a fractional elliptic equation with critical exponent in \(\mathbb {R}^n\)
• Mountain pass solutions for non-local elliptic operators
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Perturbation of \(\Delta u+u^{(N+2)/(N-2)}=0\), the scalar curvature problem in \(\mathbb{R}^N\), and related topics
• Combined effects of concave and convex nonlinearities in some elliptic problems
• Positive solutions to perturbed elliptic problems in \(\mathbb R^N\) involving critical Sobolev exponent
• Elliptic variational problems in \(\mathbb{R}^N\) with critical growth
• On the Yamabe problem and the scalar curvature problems under boundary conditions
• Best constants for Sobolev inequalities for higher order fractional derivatives
• A Brezis-Nirenberg result for non-local critical equations in low dimension
• Dual variational methods in critical point theory and applications
• Fractional Elliptic Problems with Critical Growth in the Whole of ℝn
• Regularity of the obstacle problem for a fractional power of the laplace operator
• An Extension Problem Related to the Fractional Laplacian

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