A uniqueness result for Kirchhoff type problems with singularity

DOI10.1016/J.AML.2016.03.001zbMath1344.35039OpenAlexW2301783103MaRDI QIDQ285080

Xiao-Feng Ke, Jia-Feng Liao, Chun-Yu Lei, Chun-Lei Tang

Publication date: 18 May 2016

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2016.03.001

zbMATH Keywords

uniquenesssingularityminimax methodKirchhoff type problems

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Elliptic equations and elliptic systems (35J99) Boundary value problems for functional-differential equations (34K10) Positive solutions to PDEs (35B09)

Related Items (37)

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Cites Work

• Unnamed Item
• Nontrivial solutions for Kirchhoff type equations via Morse theory
• Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents
• Existence of a positive solution to Kirchhoff-type problems without compactness conditions
• Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity
• Sign-changing solutions of a class of nonlocal quasilinear elliptic boundary value problems
• Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations in \(\mathbb R^N\)
• The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions
• A uniqueness result for a nonlocal equation of Kirchhoff type and some related open problem
• Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow
• Positive solutions for a nonlinear nonlocal elliptic transmission problem
• Resonance problems for Kirchhoff type equations
• Multiple positive solutions for Kirchhoff type problems with singularity
• Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains
• Existence and multiplicity of positive solutions for a class of Kirchhoff type problems with singularity
• The critical problem of Kirchhoff type elliptic equations in dimension four
• Infinitely many positive solutions for Kirchhoff-type problems
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• A global estimate for the gradient in a singular elliptic boundary value problem
• Combined effects of singular and superlinear nonlinearities in some singular boundary value problems.

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