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Theorems on differential inequalities and periodic boundary value problem for second-order ordinary differential equations
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SYSNO ASEP 0460328 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Theorems on differential inequalities and periodic boundary value problem for second-order ordinary differential equations Tvůrce(i) Lomtatidze, Alexander (MU-W) RID, SAI, ORCID Zdroj.dok. Memoirs on Differential Equations and Mathematical Physics - ISSN 1512-0015
Roč. 67, č. 1 (2016), s. 1-129Poč.str. 129 s. Jazyk dok. eng - angličtina Země vyd. GE - Gruzie Klíč. slova periodic boundary value problem ; positive solution ; singular equation Vědní obor RIV BA - Obecná matematika Obor OECD Applied mathematics Institucionální podpora MU-W - RVO:67985840 UT WOS 000410765300001 EID SCOPUS 84960401059 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2017
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