Recently, the existence and multiplicity results of heteroclinic orbits for a discrete pendulum equation have been investigated. In present paper, we generalize those results to a class of discrete Hamiltonian systems. Since the variational functional is identically infinite, some effective methods, provided by Rabinowitz, have to be adopted to detect critical points corresponding to heteroclinic solutions. .

By means of variational methods, we study the existence and uniqueness of almost periodic solutions for a class of second order neutral functional differential equations with infinite delay.

This paper deals with a class of impulsive periodic population evolution equations of Volterra type on Banach space. By virtue of integral inequality of Gronwall type for piecewise continuous functions, the prior estimate on the $PC$-mild solutions is derived. The compactness of the new constructed Poincaré operator is shown. This allows us to apply Horn's fixed point theorem to prove the existence of $T_{0}$-periodic $PC$-mild solutions when $PC$-mild solutions are ultimate bounded. At last, an example is given for demonstration.

In this paper we consider a class of singular differential-difference operators on the real line. We define and study the continuous wavelet transform associated with these operators. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, we establish Calderón's formulas and give practical real inversion formula for the generalized continuous wavelet transform. At the end of the paper, analogous of Heisenberg's inequality for the generalized continuous wavelet transform on Chébli-Triméche hypergroups and a special case of Jacobi-Dunkl operator are proved.

In this paper we establish the existence of solutions of infinite horizon optimal control problems with time-dependent and non-concave objective functions. We also consider an application of this problems to a forest management problem.

We use atomic decomposition and molecular characterization to show that some Calderón-Zygmund operators are bounded on $H^p_w$-boundedness for $0 < p\le 1$, where $w$ belongs to the Muckenhoup $A_1$-class.

By applying the method of weight function and techniques from Real Analysis, a Hilbert-type inequality depending upon a multi-parameter with a best constant factor is studied. The best constant is formulated in terms of a hypergeometric function. Furthermore, the inverse inequality is studied.

We are interested in the exponential stability of the zero solution of a functional dynamic equation on a time scale, a nonempty closed subset of real numbers. The approach is based on suitable Lyapunov functionals and certain inequalities. We apply our results to obtain exponential stability in Volterra integrodynamic equations on time scales.

We establish some Filippov type existence theorems for solutions of certain nonconvex fractional hyperbolic differential inclusions involving Caputo's fractional derivative.

We prove that if the solution of a general family of Boussinesq systems has a compact support for all time, then that solution vanishes identically. .