Search results for: Ireneusz Kubiaczyk

Items from 1 to 9 out of 9 results

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

Ahmet Yantir, Ireneusz Kubiaczyk, Aneta Sikorska-Nowak

Open Mathematics > 2015 > 13 > 1

In this paper, we present the existence result for Carathéodory type solutions for the nonlinear Sturm- Liouville boundary value problem (SLBVP) in Banach spaces on an arbitrary time scale. For this purpose, we introduce an equivalent integral operator to the SLBVP by means of Green’s function on an appropriate set. By imposing the regularity conditions expressed in terms of Kuratowski measure of...

article

Weak solutions for the dynamic Cauchy problem in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk, Aneta Sikorska-Nowak, Ahmet Yantir

Nonlinear Analysis > 2009 > 71 > 7-8 > 2936-2943

This paper is devoted to unify and extend the results of the existence of the weak solutions of continuous and discrete Cauchy problem in Banach spaces. We offer the existence of the weak solution of dynamic Cauchy problem on an infinite time scale. The measure of weak noncompactness and the fixed point theorem of Kubiaczyk are used to prove the main result.

article

Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals

Ireneusz Kubiaczyk, Aneta Sikorska-Nowak

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 2009 > 29 > 1 > 113-126

In the paper, we prove the existence of solutions and Carathéodory's type solutions of the dynamic Cauchy problem$x^Δ(t) = f(t,x(t))$, t ∈ T,x(0) = x₀,where T denotes an unbounded time scale (a nonempty closed subset of R and such that there exists a sequence (xₙ) in T and xₙ → ∞) and f is continuous or satisfies Carathéodory's conditions and some conditions expressed in terms of measures of noncompactness...

article

Oscillation of nonlinear neutral delay differential equations of second order

Ireneusz Kubiaczyk, Samir Saker

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 2002 > 22 > 2 > 185-212

Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear case...

article

Differential equations in banach space and henstock-kurzweil integrals

Ireneusz Kubiaczyk, Aneta Sikorska

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 1999 > 19 > 1-2 > 35-43

In this paper, using the properties of the Henstock-Kurzweil integral and corresponding theorems, we prove the existence theorem for the equation x' = f(t,x) and inclusion x' ∈ F(t,x) in a Banach space, where f is Henstock-Kurzweil integrable and satisfies some conditions.

article

Existence theorem for the Hammerstein integral equation

Mieczysław Cichoń, Ireneusz Kubiaczyk

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 1996 > 16 > 2 > 171-177

In this paper we prove an existence theorem for the Hammerstein integral equation $x(t) = p(t) + λ ∫_I K(t,s)f(s,x(s))ds$, where the integral is taken in the sense of Pettis. In this theorem continuity assumptions for f are replaced by weak sequential continuity and the compactness condition is expressed in terms of the measures of weak noncompactness. Our equation is considered in general...

article

On a fixed point theorem for weakly sequentially continuous mapping

Ireneusz Kubiaczyk

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 1995 > 15 > 1 > 15-20

Let E be a metrizable locally convex topological vector space x ∈ E, and let D be a closed convex subset of E such that x ∈ D. In this paper we prove that the weakly sequentially continuous mapping F: D ∪ D which satisfies V̅ = c̅o̅n̅v̅({x} ∪ F(V))⇒ V is relatively weakly compact, has a fixed point. Employing the above results we prove the existence theorem for the Cauchy...

article

Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk

Annales Polonici Mathematici > 1995 > 62 > 1 > 13-21

We investigate the structure of the set of solutions of the Cauchy problem x' = f(t,x), x(0) = x₀ in Banach spaces. If f satisfies a compactness condition expressed in terms of measures of weak noncompactness, and f is Pettis-integrable, then the set of pseudo-solutions of this problem is a continuum in $C_{w}(I,E)$, the space of all continuous functions from I to E endowed with the weak topology...

article

Structure of the sets of weak solutions of an ordinary differential equation in a Banach space

Ireneusz Kubiaczyk

Annales Polonici Mathematici > 1984 > 44 > 1 > 67-72

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Search results for: Ireneusz Kubiaczyk

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

Weak solutions for the dynamic Cauchy problem in Banach spaces

Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals

Oscillation of nonlinear neutral delay differential equations of second order

Differential equations in banach space and henstock-kurzweil integrals

Existence theorem for the Hammerstein integral equation

On a fixed point theorem for weakly sequentially continuous mapping

Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces

Structure of the sets of weak solutions of an ordinary differential equation in a Banach space

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