Remarks on homoclinic solutions for semilinear fourth-order ordinary differential equations without periodicity

DOI10.1007/S11766-009-1948-ZzbMath1199.34207OpenAlexW2159374105MaRDI QIDQ846785

Chengyue Li

Publication date: 12 February 2010

Published in: Applied Mathematics. Series B (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11766-009-1948-z

zbMATH Keywords

homoclinic solutionSwift-Hohenberg equationmountain pass lemmaextended Fisher-Kolmogorov equation

Mathematics Subject Classification ID

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

Related Items (16)

Infinitely many homoclinic solutions for a nonperiodic fourth-order differential equation without (AR)-condition ⋮ Unnamed Item ⋮ Ground state homoclinic solutions for a class of superquadratic fourth-order differential equations ⋮ Homoclinic solutions for a nonperiodic fourth order differential equations without coercive conditions ⋮ Existence of homoclinic orbits for a singular differential equation involving \(p\)-Laplacian ⋮ Existence of homoclinic solutions for a fourth order differential equation with a parameter ⋮ Unnamed Item ⋮ Multiplicity of homoclinic solutions for a class of nonperiodic fourth-order differential equations with general perturbation ⋮ Infinitely many homoclinic solutions for nonperiodic fourth order differential equations with general potentials ⋮ HOMOCLINIC SOLUTIONS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS WITH SUPERLINEAR NONLINEARITIES ⋮ Two homoclinic solutions of a nonperiodic fourth-order impulsive differential equation ⋮ Two homoclinic solutions for a nonperiodic fourth order differential equation with a perturbation ⋮ 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 ⋮ Concentration of homoclinic solutions for some fourth-order equations with sublinear indefinite nonlinearities

Cites Work

• A variational approach to homoclinic orbits in Hamiltonian systems
• Periodic and homoclinic solutions of some semilinear sixth-order differential equations
• Solitons due to second harmonic generation
• Existence of even homoclinic orbits for second-order Hamiltonian systems
• Homoclinic solutions for a class of the second order Hamiltonian systems
• A plethora of solitary gravity-capillary water waves with nearly critical Bond and Froude numbers
• Remarks on finding critical points
• Homoclinic orbits in the dynamic phase-space analogy of an elastic strut
• Periodic and homoclinic orbits for Lorentz-Lagranian systems via variational methods
• Homoclinic orbits for a class of Hamiltonian systems
• An introduction to minimax theorems and their applications to differential equations
• Spatial patterns. Higher order models in physics and mechanics
• Periodic and homoclinic solutions of extended Fisher-Kolmogorov equations

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