In this paper,we consider the following perturbed fractional Hamiltonian systems{tD_(∞)^(α)(_(-∞)D_(t)^(α)u(t))+L(t)u(t)=■_(u)W(t,u(t))+■(u)G(t,u(t)),t∈R,u∈H^(α)(R,R^(N)),whereα∈(1/2,1],L∈C(R,R^(N×N))...In this paper,we consider the following perturbed fractional Hamiltonian systems{tD_(∞)^(α)(_(-∞)D_(t)^(α)u(t))+L(t)u(t)=■_(u)W(t,u(t))+■(u)G(t,u(t)),t∈R,u∈H^(α)(R,R^(N)),whereα∈(1/2,1],L∈C(R,R^(N×N))is symmetric and not necessarily required to be positive definite,W∈C1(R×R^(N,R))is locally subquadratic and locally even near the origin,and perturbed term G∈C1(R×R^(N,R))maybe has no parity in u.Utilizing the perturbed method improved by the authors,a sequence of nontrivial homo clinic solutions is obtained,which generalizes previous results.展开更多
Some theorems are obtained for the existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions by the minimax methods.
基金Supported by National Natural Science Foundation of China(Grant No.12171355)Elite Scholar Program in Tianjin University,P.R.China。
文摘In this paper,we consider the following perturbed fractional Hamiltonian systems{tD_(∞)^(α)(_(-∞)D_(t)^(α)u(t))+L(t)u(t)=■_(u)W(t,u(t))+■(u)G(t,u(t)),t∈R,u∈H^(α)(R,R^(N)),whereα∈(1/2,1],L∈C(R,R^(N×N))is symmetric and not necessarily required to be positive definite,W∈C1(R×R^(N,R))is locally subquadratic and locally even near the origin,and perturbed term G∈C1(R×R^(N,R))maybe has no parity in u.Utilizing the perturbed method improved by the authors,a sequence of nontrivial homo clinic solutions is obtained,which generalizes previous results.
基金supported by the National Natural Science Foundation of China and 973 Program of STM.
文摘Some theorems are obtained for the existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions by the minimax methods.
