homoclinic orbits
Homoclinic orbits for damped vibration systems with asymptotically quadratic or subquadratic potentials
... Compared with the case where B = , the case where B = is more difficult. The study of homoclinic orbits for system (.) has attracted a lot of attention by many researchers; see [–]. This work is ...
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Ground state homoclinic orbits of damped vibration problems
... In this paper, we consider a class of non-periodic damped vibration problems with superquadratic nonlinearities. We study the existence of nontrivial ground state homoclinic orbits for this class of damped ...
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Ground state homoclinic orbits of superquadratic damped vibration systems
... , ∀t ∈ R , ∀|u| ≥ r, (.) where μ > and r > are two constants. Notice that the authors [, ] all used the condi- tion (.). Recently, Chen [, ] obtained infinitely many homoclinic orbits ...
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Existence of fast homoclinic orbits for a class of second-order non-autonomous problems
... of homoclinic orbits plays an important role in the study of the behavior of dynamical ...intersected homoclinic orbits, then it must be ...connected homoclinic orbits, then it ...
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Multiple homoclinic orbits for second order discrete Hamiltonian systems without symmetric condition
... With the aid of variational methods, the existence and multiplicity of homoclinic orbits for system (.) or its special form has been extensively investigated in many recent papers; see [–]. System ...
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Existence of periodic solutions and homoclinic orbits for third order nonlinear differential equations
... many homoclinic orbits and periodic ...the homoclinic orbits make two-dimensional ...the homoclinic orbits are filled up with the periodic ...
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Homoclinic orbits for asymptotically linear discrete Hamiltonian systems
... In recent years, several authors studied homoclinic orbits for system (.) or its special forms via critical point theory. For example, see [–]. We emphasize that in all these pa- pers the nonlinear ...
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Homoclinic orbits for a class of second order dynamic equations on time scales via variational methods
... nontrivial homoclinic orbit of the dynamic equation () by means of the mountain pass lemma and the existence of an unbounded sequence of nontrivial homoclinic orbits by using the symmetric mountain ...
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On homoclinic orbits for a class of damped vibration systems
... of homoclinic orbits for the nonperiodic system (VS) when W satisfies the subquadratic condition at ...of homoclinic orbits for the nonperiodic system (VS) when W satisfies the local (AR) growth ...
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Homoclinic orbits for second order Hamiltonian systems with asymptotically linear terms at infinity
... the homoclinic orbits of ...many homoclinic orbits by using the variant fountain theorem; Chen [] obtained the existence of a ground state homoclinic orbit for ...a homoclinic ...
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Homoclinic orbits and Lie rotated vector fields
... of homoclinic orbit as parameter is changed and the singular points are fixed on Lie rotated vector ...of homoclinic orbits that pass through saddle points on Lie rotated vector fields and the change ...
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Existence of nontrivial weak homoclinic orbits for second-order impulsive differential equations
... Motivated by the works of Nieto and Regan [], Smets and Willem [], in this paper we study the existence of nontrivial weak homoclinic orbits of (.)-(.) by using the moun- tain pass theorem, a weak ...
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Existence of homoclinic orbits for a class of p-Laplacian systems in a weighted Sobolev space
... Poincaré []. Up to the year of , a few of isolated results can be found, and the only method for dealing with such a problem was the small perturbation technique of Melnikov. Recently, the existence and multiplicity ...
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New potential condition on homoclinic orbits for a class of discrete Hamiltonian systems
... The existence and multiplicity of homoclinic solutions of system (.) or its special forms have been investigated by many authors. Papers [–] deal with the periodic case where p, L and W are periodic in n or ...
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Homoclinic orbits for second order discrete Hamiltonian systems with subquadratic potential
... respectively. In the above two cases, since L(n) is positive definite, the variational func- tional associated with system (.) is bounded from below, techniques based on the genus properties have been well applied. In ...
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Homoclinic orbits for discrete Hamiltonian systems with subquadratic potential
... In the present paper, we give a positive answer to the above question. In fact, we employ Clark’s theorem in critical point theory to establish new existence criteria to guarantee that system (.) has at least one or ...
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Infinitely many homoclinic orbits for a class of discrete Hamiltonian systems
... The existence and the multiplicity of homoclinic solutions of system (.) or its special forms have been investigated by many authors. Papers [–] deal with the periodic case, where p, L and W are N-periodic ...
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Single pulse Chaotic Dynamics in Suspended Cables with Parametric and External Excitations
... homoclinic orbits which are created by the perturbation in a resonance are obtained by using the higher-dimensional Melnikov method and extended Melnikov ...
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Multiple homoclinic solutions for p-Laplacian Hamiltonian systems with concave–convex nonlinearities
... 30 years, the existence and multiplicity of solutions for Hamiltonian systems or other dif- ferential systems have been investigated in many papers via variational methods (see [1– 4, 9, 11, 14–18, 23]). It is well-known ...
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Homoclinic solutions for second-order Hamiltonian systems with periodic potential
... distinct homoclinic orbits by using a novel varia- tional method in virtue of the famous “mountain pass” technique ...many homoclinic orbits for both superquadratic and asymp- totically ...
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