Some multiplicity results of homoclinic solutions for second order Hamiltonian systems
نویسندگان
چکیده
منابع مشابه
Existence and Multiplicity of Homoclinic Solutions for the Second Order Hamiltonian systems
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, 34...
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and Applied Analysis 3 Theorem 3. Assume that L satisfies (L) and (L) and W satisfies (W1), (W4), (W8) and (W9). Then problem (1) possesses a nontrivial homoclinic orbit. Remark 4. In Theorem 3, we consider the existence of homoclinic orbits for problem (1) under a class of local superquadratic conditions without the (AR) condition and any periodicity assumptions on both L and W. There are func...
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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 .
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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...
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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...
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ژورنال
عنوان ژورنال: Opuscula Mathematica
سال: 2020
ISSN: 1232-9274
DOI: 10.7494/opmath.2020.40.1.21