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Theorems on differential inequalities and periodic boundary value problem for second-order ordinary differential equations

SYSNO ASEP	0460328
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Theorems on differential inequalities and periodic boundary value problem for second-order ordinary differential equations
Author(s)	Lomtatidze, Alexander (MU-W)_{RID, SAI, ORCID}
Source Title	Memoirs on Differential Equations and Mathematical Physics - ISSN 1512-0015 Roč. 67, č. 1 (2016), s. 1-129
Number of pages	129 s.
Language	eng - English
Country	GE - Georgia
Keywords	periodic boundary value problem ; positive solution ; singular equation
Subject RIV	BA - General Mathematics
OECD category	Applied mathematics
Institutional support	MU-W - RVO:67985840
UT WOS	000410765300001
EID SCOPUS	84960401059
Annotation	The aim of the present article is to get efficient conditions for the solvability of the periodic boundary value problém $$ u''=f(t,u);quad u(0)=u(omega),;; u'(0)=u'(omega), $$ where the function $fcolon[0,omega]times,]0,+infty[,tobbr$ satisfies local Ca-ra-th'{e}o-do-ry conditions, i.e., it may have ''singularity'' for $u=0$. For this purpose, first the technique of differential inequalities is developed and the question on existence and uniqueness of a~positive solution of the linear problém $$ u''=p(t)u+q(t);quad u(0)=u(omega),;; u'(0)=u'(omega) $$ is studied. A~systematic application of the above-mentioned technique enables one to derive sufficient and in certain cases also necessary conditions for the solvability of the nonlinear problem considered.
Workplace	Mathematical Institute
Contact	Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
Year of Publishing	2017

Number of the records: 1