Aneta Sikorska-Nowak

Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals

We prove existence theorems for integro-differential equations 𝑥Δ∫(𝑡)=𝑓(𝑡,𝑥(𝑡),𝑡0𝑘(𝑡,𝑠,𝑥(𝑠))Δ𝑠), 𝑥(0)=𝑥0, 𝑡∈𝐼𝑎=[0,𝑎]∩𝑇, 𝑎∈𝑅

EXISTENCE OF SOLUTIONS OF THE DYNAMIC CAUCHY PROBLEM IN BANACH SPACES

Abstract In this paper we obtain the existence of solutions and Carathéodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales xΔ(t)=f(t,x(t)),x(0)=x0,t∈Ia,

On the Generalized Favard-Kantorovich and Favard-Durrmeyer Operators in Exponential Function Spaces

\matrix{{x^\Delta (t) = f(t,x(t)),} \hfill & {} \hfill \cr {x(0) = x_0 ,} \hfill & {t \in I_a ,} \hfill }

Oscillation criteria for nonlinear neutral functional dynamic equations on time scales

where f is continuous or f satisfies Carathéodory conditions and some conditions expressed in terms of measures of noncompactness. The Mönch fixed point theorem is used to prove the main result, which extends these obtained for real valued functions.

Theorems for generalized Favard-Kantorovich and Favard-Durrmeyer operators in exponential function spaces

In this paper, we first prove an existence theorem for the integrodifferential equation 8 : x 0 .t/D f t; x.t/; R t 0 k.t; s; x.s// ds

Positive solutions of perturbed nonlinear hammerstein integral equation

We consider the Kantorovich- and the Durrmeyer-type modifications of the generalized Favard operators and we prove an inverse approximation theorem for functions such that, where and,.

Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces

Abstract We propose a non-standard approach to impulsive differential equations in Banach spaces by embedding this type of problems into differential (dynamic) problems on time scales. We give an existence result for dynamic equations and, as a consequence, we obtain an existence result for impulsive differential equations.

Dynamic equations x(Δm)(t) = f(t, x(t)) on time scales

In this paper, we establish some new sufficient conditions for oscillation of the second-order neutral functional dynamic equation