We scrutinize the possibility of extending the result of [19] to the case of q-deformed oscillator for q real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two depending on whether a solution of the commutation relation is bounded or not. Our leitmotif is subnormality. The deformation parameter q is reshaped and this is what makes our approach effective. The newly arrived parameter, the operator C, has two remarkable properties: it...

The existence of optimal control for nonlinear delay systems having an implicit derivative with quadratic performance criteria is proved. The results are established by an iterative technique and using the Darbo fixed point theorem.

In this article we tackle the problem of inverse non linear ill-posed problems from a statistical point of view. We discuss the problem of estimating an indirectly observed function, without prior knowledge of its regularity, based on noisy observations. For this we consider two approaches: one based on the Tikhonov regularization procedure, and another one based on model selection methods for both ordered and non ordered subsets. In each case we prove consistency of the estimators and show...

In this paper, we study the existence of periodic solutions to a class of functional differential system. By using Schauder's fixed point theorem, we show that the system has aperiodic solution under given conditions. Finally, four examples are given to demonstrate the validity of our main results.

By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form $$x^{\text{'}}\left(t\right)+c{x}^{\text{'}}\left(t-\tau \right)=A\left(t,x\left(t\right)\right)x\left(t\right)+f\left(t,x\left(t-r_1\left(t\right)\right),\cdots ,x\left(t-r_k\left(t\right)\right)\right).$$

We consider first order neutral functional differential equations with multiple deviating arguments of the form ${(x\left(t\right)+Bx(t-\delta ))}^{\text{'}}=g₀(t,x\left(t\right))+{\sum }_{k=1}^n{g}_k(t,x(t-{\tau }_k\left(t\right)))+p\left(t\right)$. By using coincidence degree theory, we establish some sufficient conditions on the existence and uniqueness of periodic solutions for the above equation. Moreover, two examples are given to illustrate the effectiveness of our results.

By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for $n$ th order delay differential equations with damping terms $x^{\left(n\right)}\left(t\right)=\sum _{i=1}^s{b}_i{\left[x^{\left(i\right)}\left(t\right)\right]}^{2k-1}+f\left(x(t-\tau \left(t\right))\right)+p\left(t\right)$. Some new results on the existence of periodic solutions of the investigated equation are obtained.

In this paper, we consider periodic solutions for a class of nonlinear evolution equations with non-instantaneous impulses on Banach spaces. By constructing a Poincaré operator, which is a composition of the maps and using the techniques of a priori estimate, we avoid assuming that periodic solution is bounded like in [1-4] and try to present new sufficient conditions on the existence of periodic mild solutions for such problems by utilizing semigroup theory and Leray-Schauder's fixed point theorem....