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By the aids of variational methods, we study the existence of periodic and subharmonic solutions, and the minimality of their periods, for the nonautonomous first order Hamiltonian system J u ˙ (t) + ∇ H (t , u (t)) + h (t) = 0 under some kind of sublinear nonlinearity conditions. Our results are new and generalize and extend some results in the literature. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of periodic and subharmonic solutions for a class of non-autonomous first-order Hamiltonian systems such that the nonlinearity has a growth at infinity faster than $|x|^{\alpha}$, $0\leq\alpha < 1$. We also study the minimality of periods for such solutions. Our results are illustrated by specific examples. The proofs are based on the least action principle and a generalized saddle point theorem.

In this article, we prove the existence of subharmonic solutions for the non-autonomous second-order Hamiltonian system $ddot{u}(t)+V'(t,u(t))=0$. Also we study the minimality of their periods, when the nonlinearity $V'(t,x)$ grows faster than $|x|^{alpha}$, $alphain[0,1[$ at infinity. The proof is based on the Least Action Principle and the Saddle Point Theorem.

Abstract: Let be a non-constant T-periodic solution to the ordinary differential equation in a Banach space X where f is assumed to be Lipschitz continuous with constant L. Then there exists a constant c such that , with c only depending on X. It is known that in any Banach space and that in any Hilbert space, but whereas the bound of is sharp in any Hilbert space, there exists only one known example of a Banach space such that is optimal. In this paper, we show that the inequality is in fact strict in any strictly convex Banach space. Moreover, we improve the lower bound for and for a range of p close to by using a form of Wirtinger's inequality for functions in . [Copyright &y& Elsevier]

We obtain sharp bounds for minimal periods of periodic solutions to higher-order functional differential equations. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of periodic and subharmonic solutions for a class of non-autonomous first-order Hamiltonian systems such that the nonlinearity has a growth at infinity faster than |x|α, 0 ≤ α < 1. We also study the minimality of periods for such solutions. Our results are illustrated by specific examples. The proofs are based on the least action principle and a generalized saddle point theorem. [ABSTRACT FROM AUTHOR]

In this article, we prove the existence of subharmonic solutions for the non-autonomous second-order Hamiltonian system ü(t) + V'(t, u(t)) = 0. Also we study the minimality of their periods, when the nonlinearity V'(t, x) grows faster than |x|α, α ∈ [0, 1[ at infinity. The proof is based on the Least Action Principle and the Saddle Point Theorem. [ABSTRACT FROM AUTHOR]