Periodic solutions for some nonautonomous second order Hamiltonian systems

The existence and multiplicity of periodic solutions are obtained for nonautonomous second order Hamiltonian systems by the minimax methods in critical point theory.     

Periodic solutions of non-autonomous second order Hamiltonian systems

The purpose of this paper is to study the existence of periodic solutions for a class of non-autonomous second order Hamiltonian system. Some new existence theorems are obtained by the least action principle.     

Subharmonic solutions for nonautonomous sublinear second order Hamiltonian systems

Some existence theorems are obtained for subharmonic solutions of nonautonomous second order Hamiltonian systems by the minimax methods in critical point theory.     

Periodic solutions for nonautonomous second order systems with sublinear nonlinearity

The existence and multiplicity of periodic solutions are obtained for nonautonomous second order systems with sublinear nonlinearity by using the least action principle and the minimax methods.

     

Notes on periodic solutions of subquadratic second order systems

Some existence theorems are obtained for periodic solutions of the subquadratic second order systems by the minimax methods in critical point theory.     

Periodic solutions for a class of non-autonomous second order systems

The purpose of this paper is to study the existence of periodic solutions of non-autonomous second-order systems

     

Existence and multiplicity of nonzero periodic solution with saddle point character for some nonautonomous second order systems

The purpose of this paper is to study the existence and multiplicity of nonzero periodic solutions with saddle point character for the following nonautonomous second order systems:

     

Periodic solutions for a class of nonautonomous subquadratic second order Hamiltonian systems

Some existence theorems are obtained for periodic solutions of a class of unbounded nonautonomous nonconvex subquadratic second order Hamiltonian systems by using the minimax methods in critical point theory.     

Periodic solutions for second order Hamiltonian systems with a change sign potential

An existence theorem is obtained for periodic solutions of nonautonomous second order Hamiltonian systems with a change sign potential by the minimax methods in critical point theory.     

A note on periodic solutions for semi-ratio-dependent predator-prey systems

This note investigates the existence of periodic solutions for semi-ratio-dependent predator-prey models with functional response. New sharp criteria without any other nontrivial assumptions are presented by the invariance property of homotopy and analysis technique, which improve and extend many previous work. Some interesting numerical examples are given to illustrate our results.     

Positive periodic solutions of nonautonomous functional differential systems

Considered is the periodic functional differential system with a parameter, x^′(t)=A(t,x(t))x(t)+λf(t,xt). Using the eigenvalue problems of completely continuous operators, we establish some criteria on the existence of positive periodic solutions. Moreover, we apply the results to a couple of population models and obtain sufficient conditions for the existence of positive periodic solutions, which are compared with existing ones.     

Existence of periodic solutions for second-order Hamiltonian systems with asymptotically linear conditions

We consider a class of asymptotically linear nonautonomous second-order Hamiltonian systems. Using the Saddle Point Theorem, we obtain the existence result, which extends some previously known results.     

Some existence results on periodic solutions of ordinary p-Laplacian systems

Some existence theorems are obtained for periodic solutions of ordinary p-Laplacian systems by the minimax methods in critical point theory.     

A note on the optimal temporal decay estimates of solutions to the Cahn-Hilliard equation

This paper is concerned with the optimal temporal decay estimates on the solutions of the Cauchy problem of the Cahn-Hilliard equation. It is shown in Liu, Wang and Zhao (2007) [11] that such a Cauchy problem admits a unique global smooth solution u(t,x) provided that the smooth nonlinear function φ(u) satisfies a local growth condition. Furthermore if φ(u) satisfies a somewhat stronger local growth condition, the optimal temporal decay estimates on u(t,x) are also obtained in Liu, Wang and Zhao (2007) [11]. Thus a natural question is how to deduce the optimal temporal decay estimates on u(t,x) only under the local growth condition which is sufficient to guarantee the global solvability of the corresponding Cauchy problem and the main purpose of this paper is devoted to this problem. Our analysis is motivated by the technique developed recently in Ukai, Yang and Zhao (2006) [15] with a slight modification.     

Positive periodic solutions in delayed Gause-type predator-prey systems

By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of positive periodic solutions in delayed Gause-type predator-prey systems. Some known results are shown to be special cases of the presented paper.     

A note on solutions for asymptotically linear elliptic systems

In this paper, we are concerned with the elliptic system of
{ -△u＋V（x）u=g（x,v）, x∈R^N,
-△v＋V（x）v=f（x,u）, x∈R^N,
where V（x） is a continuous potential well, f, g are continuous and asymptotically linear as t→∞. The existence of a positive solution and ground state solution are established via variational methods.     

Nontrivial periodic solutions for delay differential systems via Morse theory

The existence of the nontrivial periodic solutions to the system of delay differential equations

(1.1)     

Positive periodic solutions for impulsive Gause-type predator-prey systems

This paper is devoted to impulsive periodic Gause-type predator-prey systems with monotonic or non-monotonic numerical responses. With the help of a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of positive periodic solutions. As corollaries, some applications are listed. In particular, our results improve and generalize some known ones.     

Globally exponential stability of periodic solutions for nonlinear impulsive delay systems

In this paper, the existence and globally exponential stability of periodic solutions for nonlinear impulsive delay systems are studied. Our results improve and generalize some of the previous results found in the literature. Two examples are discussed to illustrate our results.