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By using the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order self-adjoint discrete Hamiltonian system Δ[p(n)Δu(n−1)]−L(n)u(n)+∇W(n,u(n))=0 has infinitely many homoclinic orbits, where n∈Z, u∈RN, p,L:Z→RN×N and W:Z×RN→R are no periodic in n. Our conditions on the potential W(n,x) are rather relaxed. 相似文献
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In this paper, we study the problem of homoclinic orbits to Aubry sets for time-periodic positive definite Lagrangian systems. We show that there are infinitely many homoclinic orbits to some Aubry set under the conditions that the associated Mather set is uniquely ergodic and the first relative homology group of the projection of this Aubry set is nonzero. 相似文献
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Eric Paturel 《Calculus of Variations and Partial Differential Equations》2001,12(2):117-143
In this paper, we obtain the existence of at least two nontrivial homoclinic orbits for a class of second order autonomous
Hamiltonian systems. This multiplicity result is obtained by a new variational method based on the relative category: to overcome
the lack of compactness of the problem, we first solve perturbed nonautonomous problems and study the limit of the solutions
as the nonautonomous perturbation goes to 0. This method allows to get rid of some assumptions on the potential used in the
work of Ambrosetti and Coti-Zelati.
Received August 9, 1999 / Accepted September 7, 1999 / Published online September 14, 2000 相似文献
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In this paper, the existence of homoclinic orbits for the second-order Hamiltonian systems without periodicity is studied and infinitely many homoclinic orbits for both superlinear and asymptotically linear cases are obtained. 相似文献
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Some existence theorems for even homoclinic orbits are obtained for a class of second-order nonautonomous Hamiltonian systems with symmetric potentials under a class of new superquadratic conditions. A homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil-boundary-value problems which are obtained by the minimax methods. 相似文献
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Piero Montecchiari 《Annali di Matematica Pura ed Applicata》1995,168(1):317-354
We consider the Hamiltonian system q=L(t)q–V(t, q) in
R
m
,L and V being asymptotic, as t–, to certain periodic functions L_, V_. Under suitable assumptions on the functions L, L_, V, V_, we prove for any kN, the existence of infinitely many k- bump homoclinic solutions of the Hamiltonian system. 相似文献
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Supported by a CNR scholarship. Permanent address: S.I.S.S.A., strada Costiera 11, I-34014 Trieste, Italy 相似文献
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Infinitely many homoclinic orbits for a class of second‐order damped differential equations
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We investigate the existence and multiplicity of homoclinic orbits for the second‐order damped differential equations For Equation 1 where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on g, L, and W, we get infinitely many homoclinic orbits for superquadratic, subquadratic and concave–convex nonlinearities cases by using fountain theorem and dual fountain theorem in critical point theory. These results generalize and improve some existing results in the literature. Copyright © 2015 JohnWiley & Sons, Ltd. 相似文献
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