The least energy sign-changing solution for a nonlocal problem

DOI10.1063/1.4982960zbMath1365.35207OpenAlexW2612960030MaRDI QIDQ5738683

Yuanyang Yu, Fukun Zhao, Guangze Gu

Publication date: 12 June 2017

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4982960

zbMATH Keywords

sign-changing solutiondeformation lemmafractional Laplacian

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30) Diffusion processes (60J60) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)

Related Items (7)

Infinitely many positive solutions for a nonlocal problem ⋮ Infinitely many positive multi-bump solutions for fractional Kirchhoff equations ⋮ Infinitely many solutions for a class of fractional Schrödinger equations with sign-changing weight functions ⋮ Infinitely many sign-changing solutions for a nonlocal problem ⋮ Ground state and nodal solutions for fractional Kirchhoff equation with pure critical growth nonlinearity ⋮ Existence of multiple non-trivial solutions for a nonlocal problem ⋮ Existence of positive solutions for fractional Kirchhoff equation

Cites Work

• Unnamed Item
• Nonlocal diffusion and applications
• Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators
• Multiple solutions for a class of fractional Schrödinger equations in \(\mathbb{R}^N\)
• Mountain pass solutions for non-local elliptic operators
• Partial symmetry of least energy nodal solutions to some variational problems
• Energy bounds for entire nodal solutions of autonomous superlinear equations
• Variational problems with free boundaries for the fractional Laplacian
• On a class of nonlinear Schrödinger equations
• A sign-changing solution for a superlinear Dirichlet problem
• Fractional quantum mechanics and Lévy path integrals
• Minimax theorems
• Variational methods for non-local operators of elliptic type
• A Brezis-Nirenberg result for non-local critical equations in low dimension
• Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains
• Weak and viscosity solutions of the fractional Laplace equation
• Nodal and multiple solutions of nonlinear problems involving the fractional Laplacian
• Three nodal solutions of singularly perturbed elliptic equations on domains without topology
• Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting
• On the spectrum of two different fractional operators
• Nonlinear Diffusion with Fractional Laplacian Operators
• Superlinear nonlocal fractional problems with infinitely many solutions
• Fractional Elliptic Problems with Critical Growth in the Whole of ℝn
• Variational Methods for Nonlocal Fractional Problems
• The Brezis-Nirenberg result for the fractional Laplacian
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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