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

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About: Existence principle for higher-order nonlinear differential equations with state-dependent impulses via fixed point theorem Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.boundaryvalueproblems.com/content/pdf/1687-2770-2014-118.pdf
Description	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 impulses u^(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$. The impulse functions J_{ij}, i=1,...,p, j=0,...,n-1, and the barrier functions gamma_i, i = 1,...,p, are continuous on R^n and R^{n-1}, respectively. The functionals l_k, k=1,...,n, are linear and bounded on the space of left-continuous regulated (i.e. having finite one-sided limits at each point) on [a,b] vector functions. Provided the data functions h and J_{ij} are bounded, transversality conditions which guarantee that each possible solution of the problem in a given region crosses each barrier gamma_i at the unique impulse point tau_i are presented, and consequently the existence of a solution to the problem is proved. The paper provides an existence principle for a general boundary value problem of the form sum_{j=0}^{n} a_j(t) u^(j)(t) = h(t,u(t),...,u^(n-1)(t)), a.e. t in [a,b] subset R, l_k(u,u',...,u^(n-1)) = c_k, k = 1,\ldots,n, with the state dependent impulses u^(j)(t+) - u^(j)(t-) = J_{ij}(u(t-),u'(t-),...,u^(n-1)(t-)), where the impulse points t are determined as solutions of the equations t = gamma_i(u(t-),u'(t-),...,u^(n-2)(t-)), i = 1,...,p, j=0,...,n-1. Here, n,p are positive integers, c_1,..., c_n reals, the functions a_j/a_n, j=0,...,n-1, are Lebesgue integrable on [a,b] and h/a_n satisfies the Caratheodory conditions on [a,b]\R^n$. The impulse functions J_{ij}, i=1,...,p, j=0,...,n-1, and the barrier functions gamma_i, i = 1,...,p, are continuous on R^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 and J_{ij} are bounded, transversality conditions which guarantee that each possible solution of the problem in a given region crosses each barrier gamma_i at the unique impulse point tau_i are presented, and consequently the existence of a solution to the problem is proved. (en)
Title	Existence principle for higher-order nonlinear differential equations with state-dependent impulses via fixed point theorem Existence principle for higher-order nonlinear differential equations with state-dependent impulses via fixed point theorem (en)
skos:prefLabel	Existence principle for higher-order nonlinear differential equations with state-dependent impulses via fixed point theorem Existence principle for higher-order nonlinear differential equations with state-dependent impulses via fixed point theorem (en)
skos:notation	RIV/61989592:15310/14:33149125!RIV15-MSM-15310___
http://linked.open...avai/riv/aktivita	S
http://linked.open...avai/riv/aktivity	S
http://linked.open...iv/cisloPeriodika	118
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Rachůnková, Irena Tomeček, Jan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Palackého v Olomouci / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	15707
http://linked.open...ai/riv/idVysledku	RIV/61989592:15310/14:33149125
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	fixed point; transversality conditions; general linear boundary conditions; state-dependent impulses; nonlinear higher order ODE (en)
http://linked.open.../riv/klicoveSlovo	state-dependent impulses general linear boundary conditions transversality conditions fixed point nonlinear higher order ODE
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[A8CBE7920BA5]
http://linked.open...i/riv/nazevZdroje	Boundary Value Problems
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	2014
http://linked.open...iv/tvurceVysledku	Rachůnková, Irena Tomeček, Jan
http://linked.open...ain/vavai/riv/wos	000347388800003
issn	1687-2770
number of pages	15 (xsd:int)
http://bibframe.org/vocab/doi	10.1186/1687-2770-2014-118
http://localhost/t...ganizacniJednotka	15310

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