Some variants of one-dimensional and two-dimensional integral inequalities of the Volterra type are applied to study the behaviour properties of the solutions to various boundary value problems for partial differential equations of the hyperbolic type. Moreover, new types of integral inequalities for one and two variables, being a generalization of the Gronwall inequality, are presented and use...

We show existence and uniqueness of solutions stochastic path-dependent differential equations driven by cadlag martingale noise under joint local monotonicity coercivity assumptions on the coefficients with a bound in terms supremum norm. In this set-up, usual proof using ordinary Gronwall lemma together Burkholder-Davis-Gundy inequality seems impossible. order to solve problem, we prove new q...

In this paper we study existence, uniqueness and other properties of solutions Volterra type ABC fractional integral equations. We have used Banach fixed point theorem with Bielecki norm Gronwall inequality in the frame for proving our results.

In this paper we consider parametric nonlinear evolution inclusions driven by time-dependent subdiierentials. First we prove some continuous dependence results for the solution set (of both the convex and nonconvex problems) and for the set of solution-selector pairs (of the convex problem). Then we derive a continuous version of the \Filippov-Gronwall" inequality and using it, we prove the par...

In this paper, we propose a feedback control for a class of bilinear systems. Based on the Bellman-Gronwall inequality, the exponentially stable periodic solutions or limit cycles, appearing as an ellipsoid in the phase plane, are guaranteed. Moreover, the frequency of oscillation and convergence rate can be correctly estimated for such bilinear control systems. Finally, a numerical example is ...

This paper deals with almost periodic Hematopoiesis dynamic equation on time scales. By applying a novel method based on the fixed point theorem of decreasing operator, we establish sufficient conditions for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence which converges to the almost periodic positive solution. Moreover, we investigate global...