Existence of homoclinic solutions for a fourth order differential equation with a parameter

DOI10.1016/j.amc.2014.11.056zbMath1328.34038OpenAlexW2094938983WikidataQ115361405 ScholiaQ115361405MaRDI QIDQ903034

Juntao Sun, Tiexiang Li, Tsung-fang Wu

Publication date: 4 January 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.11.056

zbMATH Keywords

mountain pass theoremvariational methodshomoclinic solutionsfourth order differential equations

Mathematics Subject Classification ID

Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (14)

Existence and multiplicity of nontrivial solutions for some biharmonic equations with \(p\)-Laplacian ⋮ Unnamed Item ⋮ Travelling wave solutions of the beam equation with jumping nonlinearity ⋮ Ground state homoclinic solutions for a class of superquadratic fourth-order differential equations ⋮ Multiple solutions for generalized biharmonic equations with two singular terms ⋮ Multiple solutions for generalized biharmonic equations with singular potential and two parameters ⋮ Unnamed Item ⋮ Infinitely many periodic solutions for fourth-order impulsive differential equation with oscillatory nonlinear term ⋮ HOMOCLINIC SOLUTIONS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS WITH SUPERLINEAR NONLINEARITIES ⋮ Existence of positive ground solutions for biharmonic equations via Pohožaev-Nehari manifold ⋮ Two homoclinic solutions of a nonperiodic fourth-order impulsive differential equation ⋮ Homoclinic solutions for a class of nonlinear fourth order \(p\)-Laplacian differential equations ⋮ Existence of homoclinic solutions for a nonlinear fourth order \(p\)-Laplacian difference equation ⋮ Infinitely many homoclinic solutions for fourth-order differential equations with locally defined potentials

Cites Work

• Unnamed Item
• Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations
• Remarks on homoclinic solutions for semilinear fourth-order ordinary differential equations without periodicity
• Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations
• Two homoclinic solutions for a nonperiodic fourth order differential equation with a perturbation
• Heteroclinic solutions for the extended Fisher-Kolmogorov equation
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Homoclinic orbits in the dynamic phase-space analogy of an elastic strut
• Periodic and homoclinic orbits for Lorentz-Lagranian systems via variational methods
• Spatial patterns. Higher order models in physics and mechanics
• Periodic and homoclinic solutions of extended Fisher-Kolmogorov equations

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