Homoclinic orbits for first-order Hamiltonian system with local super-quadratic growth condition. Issue 4 (3rd April 2022)

• Record Type: Journal Article
• Authors: Zhang, Wen; Yang, Gang; Liao, Fangfang
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 4(2022)
• Page Start: 988
• Page End: 1011
• Publication Date: 2022-04-03
• Subjects: V. Radulescu; Hamiltonian system -- homoclinic orbits -- local super-quadratic condition; 37J45 -- 70H05; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1857373
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : In this paper we study the first-order Hamiltonian system 1 z ˙ = J H z ( t, z ) . Moreover precisely, assuming that the nonlinearity satisfies a local super-quadratic condition, which is weaker than the usual global super-quadratic condition, we obtain new existence results of ground state homoclinic orbits and infinitely many geometrically distinct homoclinic orbits by using a variational method. An interesting problem is that the nonlinearity may be super-quadratic on some domains and asymptotically quadratic on other domains under local super-quadratic condition. Since we are without more global information on the nonlinearity, we apply a perturbation approach and some special techniques in the proofs.