The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neit...The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neither a quadratic form in x nor periodic in t and W（t, x） is superquadratic in x.展开更多
The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two resu...The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two results about infinitely many periodic solutions of the systems extend some previously known results.展开更多
A class of second order non-autonomous Hamiltonian systems with asymptotically quadratic conditions is considered in this paper.Using Fountain Theorem,one multiplicity result of periodic solutions is obtained,which im...A class of second order non-autonomous Hamiltonian systems with asymptotically quadratic conditions is considered in this paper.Using Fountain Theorem,one multiplicity result of periodic solutions is obtained,which improves some previous results.展开更多
The authors study the existence of periodic solutions with prescribed minimal period for su-perquadratic and asymptotically linear autonomous second order Hamiltonian systems withoutany convexity assumption. Using the...The authors study the existence of periodic solutions with prescribed minimal period for su-perquadratic and asymptotically linear autonomous second order Hamiltonian systems withoutany convexity assumption. Using the variational methods, an estimate on the minimal periodof the corresponding nonconstant periodic solution of the above-mentioned system is obtained.展开更多
In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systemsü(t)-L(t)u(t)+▽uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,w...In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systemsü(t)-L(t)u(t)+▽uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,where L∈C(R,RN×N)is symmetric but non-periodic,W∈C1(R×RN,R)is locally even in u and only satisfies some growth conditions near u=0,which improves some previous results.展开更多
§ 1. IntroductionIn the present paper, we study following Hamiltonian system of Second-order:(1) with the boundary conditionx (0) = x (2jr) , x’ (0) = x’ (2w) ,(2)where p(t) ￡O(R, Rn"), G(t, x) ￡O(RxR...§ 1. IntroductionIn the present paper, we study following Hamiltonian system of Second-order:(1) with the boundary conditionx (0) = x (2jr) , x’ (0) = x’ (2w) ,(2)where p(t) ￡O(R, Rn"), G(t, x) ￡O(RxR", R). P(-) and &( , x) are 25F-periodio functions. Vj, or G’x(t, a/) will denote the gradient with respect to x. Moreover, we shall always assume that G’x(t, x) is continuous.展开更多
基金Supported by National Natural Science Foundation of China (10771173)
文摘The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neither a quadratic form in x nor periodic in t and W（t, x） is superquadratic in x.
基金Supported by National Natural Science Foundation of China (11371276,10901118)Elite Scholar Program in Tianjin University,P.R.China
文摘The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two results about infinitely many periodic solutions of the systems extend some previously known results.
基金Supported by National Natural Science Foundation of China(Grant Nos.11371276,10901118)Elite Scholar Program in Tianjin University,P.R.China
文摘A class of second order non-autonomous Hamiltonian systems with asymptotically quadratic conditions is considered in this paper.Using Fountain Theorem,one multiplicity result of periodic solutions is obtained,which improves some previous results.
文摘The authors study the existence of periodic solutions with prescribed minimal period for su-perquadratic and asymptotically linear autonomous second order Hamiltonian systems withoutany convexity assumption. Using the variational methods, an estimate on the minimal periodof the corresponding nonconstant periodic solution of the above-mentioned system is obtained.
基金National Natural Science Foundation of China(Grant No.10901118)Elite Scholar Program in Tianjin University,P.R.China。
文摘In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systemsü(t)-L(t)u(t)+▽uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,where L∈C(R,RN×N)is symmetric but non-periodic,W∈C1(R×RN,R)is locally even in u and only satisfies some growth conditions near u=0,which improves some previous results.
文摘§ 1. IntroductionIn the present paper, we study following Hamiltonian system of Second-order:(1) with the boundary conditionx (0) = x (2jr) , x’ (0) = x’ (2w) ,(2)where p(t) ￡O(R, Rn"), G(t, x) ￡O(RxR", R). P(-) and &( , x) are 25F-periodio functions. Vj, or G’x(t, a/) will denote the gradient with respect to x. Moreover, we shall always assume that G’x(t, x) is continuous.
