Existence principle for higher-order nonlinear differential equations with state-dependent impulses via fixed point theorem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F14%3A33149125" target="_blank" >RIV/61989592:15310/14:33149125 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.boundaryvalueproblems.com/content/pdf/1687-2770-2014-118.pdf" target="_blank" >http://www.boundaryvalueproblems.com/content/pdf/1687-2770-2014-118.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1186/1687-2770-2014-118" target="_blank" >10.1186/1687-2770-2014-118</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Existence principle for higher-order nonlinear differential equations with state-dependent impulses via fixed point theorem

Popis výsledku v původním jazyce

The paper provides an existence principle for a general boundary value problem of the form sum_{j=0}^{n} a_j(t) u^(j)(t) = h(t,u(t),...,u^(n-1)(t)), a.e. t in [a,b] subset R, l_k(u,u',...,u^(n-1)) = c_k, k = 1,ldots,n, with the state dependent impulsesu^(j)(t+) - u^(j)(t-) = J_{ij}(u(t-),u'(t-),...,u^(n-1)(t-)), where the impulse points t are determined as solutions of the equations t = gamma_i(u(t-),u'(t-),...,u^(n-2)(t-)), i = 1,...,p, j=0,...,n-1. Here, n,p are positive integers, c_1,..., c_n reals, the functions a_j/a_n, j=0,...,n-1, are Lebesgue integrable on [a,b] and h/a_n satisfies the Caratheodory conditions on [a,b]R^n$. The impulse functions J_{ij}, i=1,...,p, j=0,...,n-1, and the barrier functions gamma_i, i = 1,...,p, are continuous onR^n and R^{n-1}, respectively. The functionals l_k, k=1,...,n, are linear and bounded on the space of left-continuous regulated (i.e. having finite one-sided limits at each point) on [a,b] vector functions. Provided the data functions h a

Název v anglickém jazyce

Existence principle for higher-order nonlinear differential equations with state-dependent impulses via fixed point theorem

Popis výsledku anglicky

The paper provides an existence principle for a general boundary value problem of the form sum_{j=0}^{n} a_j(t) u^(j)(t) = h(t,u(t),...,u^(n-1)(t)), a.e. t in [a,b] subset R, l_k(u,u',...,u^(n-1)) = c_k, k = 1,ldots,n, with the state dependent impulsesu^(j)(t+) - u^(j)(t-) = J_{ij}(u(t-),u'(t-),...,u^(n-1)(t-)), where the impulse points t are determined as solutions of the equations t = gamma_i(u(t-),u'(t-),...,u^(n-2)(t-)), i = 1,...,p, j=0,...,n-1. Here, n,p are positive integers, c_1,..., c_n reals, the functions a_j/a_n, j=0,...,n-1, are Lebesgue integrable on [a,b] and h/a_n satisfies the Caratheodory conditions on [a,b]R^n$. The impulse functions J_{ij}, i=1,...,p, j=0,...,n-1, and the barrier functions gamma_i, i = 1,...,p, are continuous onR^n and R^{n-1}, respectively. The functionals l_k, k=1,...,n, are linear and bounded on the space of left-continuous regulated (i.e. having finite one-sided limits at each point) on [a,b] vector functions. Provided the data functions h a

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

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Návaznosti

S - Specificky vyzkum na vysokych skolach

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

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Svazek periodika

2014

Číslo periodika v rámci svazku

118

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

15

Strana od-do

1-15

Kód UT WoS článku

000347388800003

EID výsledku v databázi Scopus

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