Rong Yuan, Ziheng Zhang
Abstract:
This article studies the existence of homoclinic solutions
for the second-order non-autonomous Hamiltonian system
where
is a symmetric and positive
definite matrix for all
.
The function
is not assumed to satisfy the global Ambrosetti-Rabinowitz
condition. Assuming reasonable conditions on
and
,
we prove the existence of at least one nontrivial homoclinic solution,
and for
even in
, we prove the existence of infinitely
many homoclinic solutions.
Submitted January 14, 2010. Published February 25, 2010.
Math Subject Classifications: 34C37, 35A15, 37J45.
Key Words: Homoclinic solutions; critical point; variational methods;
mountain pass theorem.
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Rong Yuan School of Mathematical Sciences, Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education, Beijing 100875, China email: ryuan@bnu.edu.cn | |
Ziheng Zhang School of Mathematical Sciences, Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education, Beijing 100875, China email: zhzh@mail.bnu.edu.cn |
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