Homoclinic solutions for a class of non-autonomous subquadratic second-order Hamiltonian systems

Abstract In this paper we consider the existence of homoclinic solutions for the following second-order non-autonomous Hamiltonian system: (HS) q − L ( t ) q + W q ( t , q ) = 0 , where L ( t ) ∈ C ( R , R n 2 ) is a symmetric and positive definite matrix for all t ∈ R , W ( t , q ) = a ( t ) | q | γ with a ( t ) : R → R + is a positive continuous function and 1 γ 2 is a constant. Adopting some other reasonable assumptions for L and W , we obtain a new criterion for guaranteeing that (HS) has one nontrivial homoclinic solution by use of a standard minimizing argument in critical point theory. Recent results from the literature are generalized and significantly improved.

[1]  Claudianor Oliveira Alves,et al.  Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation , 2003, Appl. Math. Lett..

[2]  Paulo Cesar Carrião,et al.  Existence of homoclinic solutions for a class of time-dependent Hamiltonian systems , 1999 .

[3]  Vittorio Coti Zelati,et al.  Multiple homoclinic orbits for a class of conservative systems , 1993 .

[4]  Vittorio Coti Zelati,et al.  Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials , 1991 .

[5]  Alan C. Lazer,et al.  Homoclinic Orbits for a Class of Symmetric Hamiltonian Systems , 1994 .

[6]  Ying Lv,et al.  Existence of even homoclinic orbits for second-order Hamiltonian systems , 2007 .

[7]  P. Rabinowitz,et al.  Some results on connecting orbits for a class of Hamiltonian systems , 1991 .

[8]  Paul H. Rabinowitz.  Homoclinic orbits for a class of Hamiltonian systems , 1990 .

[9]  P. Rabinowitz,et al.  Dual variational methods in critical point theory and applications , 1973 .

[10]  Ding Yanheng,et al.  Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems , 1995 .

[11]  Eric Paturel.  Multiple homoclinic orbits for a class of Hamiltonian systems , 2001 .

[12]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[13]  Marek Izydorek,et al.  Homoclinic solutions for a class of the second order Hamiltonian systems , 2005 .

[14]  M. Willem,et al.  Homoclinic orbits for a class of Hamiltonian systems , 1992, Differential and Integral Equations.

[15]  P. Rabinowitz.  Minimax methods in critical point theory with applications to differential equations , 1986 .

[16]  Yanheng Ding,et al.  Periodic and homoclinic solutions to a class of Hamiltonian systems with the potentials changing sign , 1993 .