Under some local superquadratic conditions on <em>W</em> (<em>t</em>, <em>u</em>) with respect to <em>u</em>, the existence of infinitely many solutions is obtained for ...Under some local superquadratic conditions on <em>W</em> (<em>t</em>, <em>u</em>) with respect to <em>u</em>, the existence of infinitely many solutions is obtained for the nonperiodic fractional Hamiltonian systems<img src="Edit_b2a2ac0a-6dde-474f-8c75-e9f5fc7b9918.bmp" alt="" />, where <em>L</em> (<em>t</em>) is unnecessarily coercive.展开更多
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
文摘Under some local superquadratic conditions on <em>W</em> (<em>t</em>, <em>u</em>) with respect to <em>u</em>, the existence of infinitely many solutions is obtained for the nonperiodic fractional Hamiltonian systems<img src="Edit_b2a2ac0a-6dde-474f-8c75-e9f5fc7b9918.bmp" alt="" />, where <em>L</em> (<em>t</em>) is unnecessarily coercive.
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.
