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
In this paper, we prove the existence of nontrivial homoclinic orbits for a class of Hamiltonian systems with potential changing sign. We use Mountain Pass Lemma.
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
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
Combining the dual least action principle with Mountain-pass lemma,we obtain the existence of brake orbits for first-order convex Hamiltonian systems with particular anisotropic growth.
This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L（t）z＋Wz（t,z）=0,where L∈C（R,RN2）is a symmetric matrix-valued function and W（t,z）∈C1（R×RN,R）is a...This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L（t）z＋Wz（t,z）=0,where L∈C（R,RN2）is a symmetric matrix-valued function and W（t,z）∈C1（R×RN,R）is a nonlinear term.Since there are no periodic assumptions on L（t）and W（t,z）in t,one should overcome difficulties for the lack of compactness of the Sobolev embedding.Moreover,the nonlinearity W（t,z）is asymptotically linear in z at infinity and the system is allowed to be resonant,which is a case that has never been considered before.By virtue of some generalized mountain pass theorem,multiple homoclinic orbits are obtained.展开更多
In this paper, we apply a variant of the famous Mountain Pass Lemmas of Ambrosetti-Rabinowitz and Ambrosetti-Coti Zelati with （PSC）c type condition of Palais-Smale-Cerami to study the existence of new periodic solut...In this paper, we apply a variant of the famous Mountain Pass Lemmas of Ambrosetti-Rabinowitz and Ambrosetti-Coti Zelati with （PSC）c type condition of Palais-Smale-Cerami to study the existence of new periodic solutions with a prescribed energy for symmetrical singular second order Hamiltonian conservative systems with weak force type potentials.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This work is mainly supported by National Natural Science Foundation of China (No.10371007) 15th Scientific Research Foundation of Central University for Nationalities.
文摘In this paper, we prove the existence of nontrivial homoclinic orbits for a class of Hamiltonian systems with potential changing sign. We use Mountain Pass Lemma.
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.
基金supported by the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2019L0766)the Doctoral Scientific Research Foundation of Shanxi Datong University+1 种基金supported by NNSF of China(Grant Nos.11471170 and 11790271)innovation and development project of Guangzhou University,and Nankai Zhide Foundation
文摘Combining the dual least action principle with Mountain-pass lemma,we obtain the existence of brake orbits for first-order convex Hamiltonian systems with particular anisotropic growth.
文摘This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L（t）z＋Wz（t,z）=0,where L∈C（R,RN2）is a symmetric matrix-valued function and W（t,z）∈C1（R×RN,R）is a nonlinear term.Since there are no periodic assumptions on L（t）and W（t,z）in t,one should overcome difficulties for the lack of compactness of the Sobolev embedding.Moreover,the nonlinearity W（t,z）is asymptotically linear in z at infinity and the system is allowed to be resonant,which is a case that has never been considered before.By virtue of some generalized mountain pass theorem,multiple homoclinic orbits are obtained.
基金Supported by National Natural Science Foundation of China(Grant No.11071175)National Research Foundation for the Doctoral Program of Ministry of Education of China
文摘In this paper, we apply a variant of the famous Mountain Pass Lemmas of Ambrosetti-Rabinowitz and Ambrosetti-Coti Zelati with （PSC）c type condition of Palais-Smale-Cerami to study the existence of new periodic solutions with a prescribed energy for symmetrical singular second order Hamiltonian conservative systems with weak force type potentials.
