On the existence of homoclinic type solutions of inhomogenous Lagrangian\n systems

2017/02/04 by Jakub Ciesielski, Ciesielski, Jakub, Joanna Janczewska +3
Mathematics · #Nonlinear Differential Equations Analysis #Differential Equations and Boundary Problems #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.1702.01346

Abstract

We study the existence of homoclinic type solutions for second order\nLagrangian systems of the type \q(t)-q(t)+a(t)\∇ G(q(t))=f(t),\nwhere t\∈\ℝ, q\∈\ℝⁿ, a colon\ℝ\→\ℝ is\na continuous positive bounded function, G colon\ℝⁿ\→\ℝ is a\nC¹-smooth potential satisfying the Ambrosetti-Rabinowitz superquadratic\ngrowth condition and f colon\ℝ\→\ℝⁿ is a continuous bounded\nsquare integrable forcing term. A homoclinic type solution is obtained as limit\nof 2k-periodic solutions of an approximative sequence of second order\ndifferential equations.\n

Related

• On the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems
• Infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems
• Heteroclinic and homoclinic solutions for nonlinear second-order coupled systems with phi-Laplacians
• Existence of homoclinic solution in first order discrete Hamiltonian system
• Existence and multiplicity of Homoclinic solutions for the second order Hamiltonian systems