Fixed point problem associated with state-dependent impulsive boundary value problems

Kód výsledku v IS VaVaI

RIV/61989592:15310/14:33149758 - isvavai.cz

Výsledek na webu

http://www.boundaryvalueproblems.com/content/2014/1/172

DOI - Digital Object Identifier

10.1186/s13661-014-0172-9

Jazyk výsledku

angličtina

Název v původním jazyce

Fixed point problem associated with state-dependent impulsive boundary value problems

Popis výsledku v původním jazyce

The paper investigates a fixed point problem in the space W([a,b];R^n)^(p+1) which is connected to boundary value problems with state-dependent impulses of the form z'(t) = f(t,z(t)), a.e. t in [a,b] subset R z(t_i+) - z(t_i) = J_i(t_i,z(t_i)), i = 1,...,n ell(z) = c_0. Here, the impulse instants t_i are determined as solutions of the equations t_i = gamma_i(z(t_i)), i = 1,...,p. We assume that n,p in N, c_0 in R^n, the vector function f satisfies the Caratheodory conditions on [a,b]xR^n, the impulse functions J_i, i=1,...,p, are continuous on [a,b]xR^n, and the barrier functions gamma_i, i = 1,...,p, are continuous on R^n. The operator ell is an arbitrary linear and bounded operator on the space of left-continuous regulated on [a,b] vector valued functions and is represented by the Kurzweil-Stieltjes integral. Provided the data functions f and J_i are bounded, transversality conditions which guarantee that this fixed point problem is solvable are presented. As a result it is possible

Název v anglickém jazyce

Fixed point problem associated with state-dependent impulsive boundary value problems

Popis výsledku anglicky

The paper investigates a fixed point problem in the space W([a,b];R^n)^(p+1) which is connected to boundary value problems with state-dependent impulses of the form z'(t) = f(t,z(t)), a.e. t in [a,b] subset R z(t_i+) - z(t_i) = J_i(t_i,z(t_i)), i = 1,...,n ell(z) = c_0. Here, the impulse instants t_i are determined as solutions of the equations t_i = gamma_i(z(t_i)), i = 1,...,p. We assume that n,p in N, c_0 in R^n, the vector function f satisfies the Caratheodory conditions on [a,b]xR^n, the impulse functions J_i, i=1,...,p, are continuous on [a,b]xR^n, and the barrier functions gamma_i, i = 1,...,p, are continuous on R^n. The operator ell is an arbitrary linear and bounded operator on the space of left-continuous regulated on [a,b] vector valued functions and is represented by the Kurzweil-Stieltjes integral. Provided the data functions f and J_i are bounded, transversality conditions which guarantee that this fixed point problem is solvable are presented. As a result it is possible

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

GA14-06958S: Singularity a impulsy v okrajových úlohách pro nelineární obyčejné diferenciální rovnice

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Boundary Value Problems

ISSN

1687-2770

e-ISSN

—

Svazek periodika

2014

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

17

Strana od-do

1-17

Kód UT WoS článku

000347394300002

EID výsledku v databázi Scopus

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