The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,...The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.展开更多
In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity the...In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.展开更多
In this paper we study the existence of infinitely many periodic solutions for second-order Hamiltonian systems{ü（t）＋A（t）u（t）＋▽F（t,u（t））=0,u（0）-u（T）=u^·（0）-u^·（T）=0,where F（t,u） i...In this paper we study the existence of infinitely many periodic solutions for second-order Hamiltonian systems{ü（t）＋A（t）u（t）＋▽F（t,u（t））=0,u（0）-u（T）=u^·（0）-u^·（T）=0,where F（t,u） is even in u,and ▽（t,u） is of sublinear growth at infinity and satisfies the Ahmad-Lazer-Paul condition.展开更多
In this paper, we are concerned with the existence of periodic solutions of second-order non-autonomous systems. By applying the Schauder＇s fixed point theorem and Miranda＇s theorem, a new existence result of period...In this paper, we are concerned with the existence of periodic solutions of second-order non-autonomous systems. By applying the Schauder＇s fixed point theorem and Miranda＇s theorem, a new existence result of periodic solutions is established.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
文摘The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.
基金Supported by the Youth Foundation of Shangqiu Institute of Technology(No.2018XKQ01)
文摘In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.
基金Supported by NSF of Education Committee of Henan province(12B11026)NSF of Henan province(132300410341,122300410034,132300410056)Nanhu Scholars Program for Young Scholars of XYNU
文摘In this paper we study the existence of infinitely many periodic solutions for second-order Hamiltonian systems{ü（t）＋A（t）u（t）＋▽F（t,u（t））=0,u（0）-u（T）=u^·（0）-u^·（T）=0,where F（t,u） is even in u,and ▽（t,u） is of sublinear growth at infinity and satisfies the Ahmad-Lazer-Paul condition.
基金Supported by the Fundamental Research Funds for the Gansu Universities(2015A-150)the PhD scientific research start-up capital funded projects of Longdong University(XYBY05)
文摘In this paper, we are concerned with the existence of periodic solutions of second-order non-autonomous systems. By applying the Schauder＇s fixed point theorem and Miranda＇s theorem, a new existence result of periodic solutions is established.
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.
