Homoclinic orbits of nonperiodic superquadratic Hamiltonian system. (English) Zbl 1321.37065

Zhang, Jian; Tang, Xianhua; Zhang, Wen

Taiwanese J. Math. 17, No. 6, 1855-1867 (2013).

For a first-order nonperiodic Hamiltonian system \(\dot z=\mathcal J H_z(t,z)\) with \(H(t,z)=\frac 12 L(t)z\cdot z+R(t,z)\), under a series assumptions on the nonlinearity including the weak superquadratic condition, the authors prove the existence of at least one homoclinic orbit, which is a ground state solution of the Hamiltonian system, in a variational setting and using the method of the generalized Nehari manifold.

Reviewer: Xiang Zhang (Shanghai)

MSC:

37K05	Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37J45	Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
70K44	Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics

Keywords:

first-order Hamiltonian system; homoclinic orbits; ground state solutions; generalized Nehari manifold