HOMOCLINIC SOLUTIONS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS WITH SUPERLINEAR NONLINEARITIES

DOI10.11948/2018.66zbMath1459.34111OpenAlexW2782908776MaRDI QIDQ5147802

Zhisu Liu, Ziheng Zhang

Publication date: 28 January 2021

Published in: Journal of Applied Analysis & Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11948/2018.66

zbMATH Keywords

variational methodscritical pointhomoclinic solutionsFountain theorem

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Nonautonomous smooth dynamical systems (37C60)

Cites Work

• Infinitely many homoclinic solutions for a nonperiodic fourth-order differential equation without (AR)-condition
• Remarks on homoclinic solutions for semilinear fourth-order ordinary differential equations without periodicity
• Homoclinic solutions for a nonperiodic fourth order differential equations without coercive conditions
• Existence of homoclinic solutions for a fourth order differential equation with a parameter
• On the existence of solutions for a class of fourth order differential equations
• Homoclinic orbits of two classes of fourth order semilinear differential equations with periodic nonlinearity
• Infinitely many homoclinic solutions for nonperiodic fourth order differential equations with general potentials
• Minimax theorems
• Solitons due to second harmonic generation
• Two homoclinic solutions for a nonperiodic fourth order differential equation with a perturbation
• Concentration of homoclinic solutions for some fourth-order equations with sublinear indefinite nonlinearities
• A plethora of solitary gravity-capillary water waves with nearly critical Bond and Froude numbers
• Homoclinic orbits in the dynamic phase-space analogy of an elastic strut
• Homoclinic orbits for a special class of non autonomous Hamiltonian systems
• 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