Existence and Multiplicity of Homoclinic Solutions for the Second Order Hamiltonian systems
نویسندگان
چکیده
In this paper we study the existence and multiplicity of homoclinic solutions for the second order Hamiltonian system ü−L(t)u(t)+Wu(t, u) = 0, ∀t ∈ R, by means of the minmax arguments in the critical point theory, where L(t) is unnecessary uniformly positively definite for all t ∈ R and Wu(t, u) sastisfies the asymptotically linear condition. Mathematics Subject Classification: 37J45, 58E05, 34C37, 70H05
منابع مشابه
Multiplicity of Homoclinic Solutions for Fractional Hamiltonian Systems with Subquadratic Potential
In this paper, we study the existence of homoclinic solutions for the fractional Hamiltonian systems with left and right Liouville–Weyl derivatives. We establish some new results concerning the existence and multiplicity of homoclinic solutions for the given system by using Clark’s theorem from critical point theory and fountain theorem.
متن کاملExistence of Homoclinic Solutions for Second Order Hamiltonian Systems under Local Conditions
Under some local conditions on V(t,x) with respect to x , the existence of homoclinic solutions is obtained for a class of the second order Hamiltonian systems ü(t) +∇V(t,u(t)) = f (t), ∀t ∈ R .
متن کاملHomoclinic solutions for second order Hamiltonian systems with general potentials near the origin∗
In this paper, we study the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems with general potentials near the origin. Recent results from the literature are generalized and significantly improved.
متن کاملHomoclinic solutions for a class of non-periodic second order Hamiltonian systems
We study the existence of homoclinic solutions for the second order Hamiltonian system ü+Vu(t, u) = f(t). Let V (t, u) = −K(t, u)+W (t, u) ∈ C1(R×Rn,R) be T -periodic in t, where K is a quadratic growth function and W may be asymptotically quadratic or super-quadratic at infinity. One homoclinic solution is obtained as a limit of solutions of a sequence of periodic second order differential equ...
متن کاملHomoclinic Solutions for Second-order Non-autonomous Hamiltonian Systems without Global Ambrosetti-rabinowitz Conditions
This article studies the existence of homoclinic solutions for the second-order non-autonomous Hamiltonian system q̈ − L(t)q + Wq(t, q) = 0, where L ∈ C(R, Rn ) is a symmetric and positive definite matrix for all t ∈ R. The function W ∈ C1(R × Rn, R) is not assumed to satisfy the global Ambrosetti-Rabinowitz condition. Assuming reasonable conditions on L and W , we prove the existence of at leas...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010