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Existence of infinitely many homoclinic orbits in Hamiltonian systems

Published online by Cambridge University Press:  26 September 2011

X. H. Tang  and
Xiaoyan Lin
X. H. Tang
Affiliation:
School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, People's Republic of China ([email protected])
Xiaoyan Lin
Affiliation:
School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, People's Republic of China ([email protected]) and Department of Mathematics, Huaihua College, Huaihua, Hunan 418008, People's Republic of China
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Abstract

By using the symmetric mountain pass theorem, we establish some new existence criteria to guarantee that the second-order Hamiltonian systems ü(t) − L(t)u(t) + ∇W(t,u(t)) = 0 have infinitely many homoclinic orbits, where t ∈ ℝ, u ∈ ℝN, L ∈ C(ℝ, ℝN × N) and W ∈ C1(ℝ × ℝN, ℝ) are not periodic in t. Our results generalize and improve some existing results in the literature by relaxing the conditions on the potential function W(t, x).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 5 , October 2011 , pp. 1103 - 1119
Copyright
Copyright © Royal Society of Edinburgh 2011

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