[PDF] Top 20 New homoclinic solutions for a class of second-order Hamiltonian systems with a mixed condition

... of homoclinic orbits for problem (1) such as [1, 3–18, ...periodic condition, Rabinowitz and Tanaka [21] introduced the following coercive condition on ... See full document

... The homoclinic solutions have been proved to be important in studying the behavior of dynamic ...periodic solutions. In order to get the compactness of embedding theorem back, many conditions ... See full document

... 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 quadratic ...common ... See full document

... of homoclinic solutions for a class of second order p-Laplacian systems with impulsive ...A new result is obtained under more relaxed conditions by using the mountain pass ... See full document

... the second order self-adjoint discrete Hamiltonian system [p(n) u(n – 1)] – L(n)u(n) + λ a(n)∇G(u(n)) + μ b(n)∇ F(u(n)) = 0, where p,L : Z → R N×N are both positive definite for all n ∈ Z, and no ... See full document

... of homoclinic solutions and periodic solutions for Hamiltonian systems have been extensively studied by critical point ...considered homoclinic solutions for the special ... See full document

... periodic solutions for problem ...potential condition (see []), the convex type potential condition (see []), the periodic type potential conditions (see []), the even type potential ... See full document

... a new method to study the existence and multiplicity of periodic solutions of difference equations by using critical point theory (see [–]), the ex- istence and multiplicity of periodic solutions ... See full document

... subharmonic solutions to the p-Laplacian systems of ...subharmonics solutions of p-Laplacian system by using the dual least action ...periodic solutions obtained in this paper slightly ... See full document

... Some new existence theorems for homoclinic solutions are obtained for a class of second-order discrete p -Laplacian systems by critical point theory, a homoclinic ... See full document

... Ambrosetti-Rabinowitz condition (A-R ...of solutions of second-order systems under condition ...of solutions for system (.) under a kind of new superquadratic ... See full document

... 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 ... See full document

... of homoclinic solutions for system ...a new direct sum decomposition of the ‘work space’, Tang and Lin proved the following theorem by using a linking theorem which was developed in ... See full document

... Remark . Obviously, the condition (H) is a special case of (H)-(H). If (H) holds, so do (H)-(H); however, the reverse is not true. W (t, q) defined in () can satisfy the conditions (H) and (H), but W (t, ... See full document

... Homoclinic solutions of dynamical systems are very important in applications for a lot of ...of homoclinic solutions for system ...many homoclinic solutions by using the ... See full document

... the condition (.), some authors studied the homoclinic orbits of ...many homoclinic orbits by using the variant fountain theorem; Chen [] obtained the existence of a ground state homoclinic ... See full document

... where μ >  and r >  are two constants. Notice that the authors [, ] all used condi- tion (.). Recently, the author in [, ] obtained infinitely many homoclinic orbits for (.) when H satisfies the ... See full document

...        uniformly in v V  . (3.24) Hence by Lemma 3.1 and properties (3.18), (3.24), we deduce that the functional  satisfies all the assump- tions of Theorem 2.1. Therefore the Hamiltonian system (࣢) ... See full document

... Lemma 3.4 Under the conditions of Theorem 1.2, F ( x ) satisfies the PS condition. Proof From the proof of Lemma 3.2, we see that it is sufficient to show that for any sequence { x ( k ) } kÎN ⊂ E such that { F ( ... See full document

... 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 ... See full document