The Existence and Multiple Periodic Solutions for Generalized Asymptotical Linear Hamiltonian Systems without Convexity Condition
نویسنده
چکیده
Abstract This paper consider the existence and multiplicity of solutions for the first order Hamiltonian systems satisfying Sturm-Liouville boundary conditions without convexity assumption. The gradient of Hamiltonian function is generalized asymptotically linear. We find critical points of the corresponding functional by verifying the assumptions of Theorems about critical points given by Bartsch and Ding in [1].
منابع مشابه
MULTIPLE PERIODIC SOLUTIONS FOR A CLASS OF NON-AUTONOMOUS AND CONVEX HAMILTONIAN SYSTEMS
In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.
متن کاملNew conditions on ground state solutions for Hamiltonian elliptic systems with gradient terms
This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...
متن کاملPERIODIC SOLUTIONS OF CERTAIN THREE DIMENSIONAL AUTONOMOUS SYSTEMS
There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...
متن کاملPeriodic solutions for second - order Hamiltonian systems with a p - Laplacian
In this paper, by using the least action principle, Sobolev’s inequality and Wirtinger’s inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature.
متن کاملA twist condition and periodic solutions of Hamiltonian systems
In this paper, we investigate existence of nontrivial periodic solutions to the Hamiltonian system −J ż=H ′(t, z), z ∈R2N . (HS) Under a general twist condition for the Hamiltonian function in terms of the difference of the Conley– Zehnder index at the origin and at infinity we establish existence of nontrivial periodic solutions. Compared with the existing work in the literature, our results d...
متن کامل