Related papers: The minimal periodic solutions for superquadratic …
Under weaker regularity and compactness assumptions, we find the mountain-pass essential point, which is a novel extension of the classical Ambrosetti-Rabinowitz mountain pass theorem. We study the reversible superquadratic autonomous…
Let $P\in Sp(2n)$ satisfying $P^{k}=I_{2n}$, we consider the minimal $P$-symmetric period problem of the autonomous nonlinear Hamiltonian system \begin{equation*} \dot x(t) = JH^{\prime}(x(t)). \end{equation*} For some symplectic matrices…
By using the variational minimizing method with a special constraint and the direct variational minimizing method without constraint, we study second order Hamiltonian systems with a singular potential $V\in C^2(R^n\backslash O,R)$ and…
In this paper some existence results for the minimal P-symmetric periodic solutions are proved for first order autonomous Hamiltonian systems when the Hamiltonian function is superquadratic, asymptotically linear and subquadratic. These are…
In this work we prove the lower bound for the number of $T$-periodic solutions of an asymptotically linear planar Hamiltonian system. Precisely, we show that such a system, $T$-periodic in time, with $T$-Maslov indices $i_0,i_\infty$ at the…
In this paper, the existence of subharmonic solutions for a class of non-autonomous first-order Hamiltonian systems is investigated. We also study the minimality of periods for such solutions. Our results which extend and improve many…
Firstly,we generalize the classical Palais-Smale-Cerami condition for $C^1$ functional to the local Lipschitz case,then generalize the famous Benci-Rabinowitz's and Rabinowitz's Saddle Point Theorems with classical Cerami-Palais-Smale…
Using a homologically link theorem in variational theory and iteration inequalities of Maslov-type index, we prove the existences of a sequence of subharmonic solutions for one type of sub-quadratic non-autonomous Hamiltonian systems.…
In this paper, we consider the minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. We prove that if the Hamiltonian function $H\in C^2(\Bbb R^{2n}, \Bbb R)$ is super-quadratic and convex, for every number…
We study connected branches of non-constant {$2\pi$-pe}riodic solutions of the Hamilton equation \begin{displaymath} \dot{x}(t)=\lambda J\nabla H(x(t)), \end{displaymath} where $\lambda\in\halfline,$ $H\in C^2(\R^n\times\R^n,\R)$ and $…
In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here…
In this paper we consider a class of planar autonomous systems having an isolated limit cycle x_0 of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We…
Aim of this paper is to investigate the existence of periodic solutions of a nonlinear planar autonomous system having a limit cycle x_0 of least period T_0>0 when it is perturbed by a small parameter, T_1-periodic, perturbation. In the…
In this paper, for any positive integer $n$, we study the Maslov-type index theory of $i_{L_0}$, $i_{L_1}$ and $i_{\sqrt{-1}}^{L_0}$ with $L_0=\{0\}\times \R^n\subset \R^{2n}$ and $L_1=\R^n\times \{0\} \subset \R^{2n}$. As applications we…
We show that a problem on minimal periods of solutions of Lipschitz functional differential equations is closely related to the unique solvability of the periodic problem for linear functional differential equations. Sharp bounds for…
This paper concerns the existence of multiple rotating quasi-periodic solutions for second order Hamiltonian systems with sub-quadratic potential. Such solutions have the form $x(t+T)=Qx(t)$ for some orthogonal matrix $Q$. To deal with such…
In this paper we prove a lower bound for the least number of one-periodic solutions of nondegenerate locally Hamiltonian equations on compact symplectic manifolds in terms of the Betti numbers of the Novikov homology associated to the…
We discuss the existence and non-existence of periodic in one variable and compactly supported in the other variables least energy solutions for equations with non-Lipschitz nonlinearity of the form: $-\Delta u=\lambda u^p - u^q$ in…
We consider Hamiltonian systems with two degrees of freedom of point vortex type \[ \kappa_j \dot{z}_j = J \nabla_{z_j} H_\Omega(z_1,z_2), \quad j=1,2, \] for $z_1,z_2$ in a domain $\Omega\subset\mathbb{R}^2$. In the classical point vortex…
In this paper we consider a class of nonlinear periodic differential systems perturbed by two nonlinear periodic terms with multiplicative different powers of a small parameter $e>0$. For such a class of systems we provide conditions which…