Oscilační a asymptotická teorie pololineárních diferenciálních rovnic

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F70883521%3A28140%2F07%3A63505887" target="_blank" >RIV/70883521:28140/07:63505887 - isvavai.cz</a>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

Oscillation and asymptotic theory of half-linear differential equations

Popis výsledku v původním jazyce

In this thesis we investigate oscillatory and asymptotic properties of solutions of the half-linear second order differential equation {*} (r(t)Phi(x'))'+c(t)Phi(x)=0 where Phi(x):=|x|^{p-1} sgn x, p>1, and r, c are continuous functions, r(t)>0. Thecentral idea which goes through the entire thesis is the concept of perturbations. We regard equation {*} as a perturbation of another half-linear equation in the same form to get some results for a class of half-linear equations for which the classicalapproach fails. We consider equation {*} as a perturbation of a general (nonoscillatory) two-term equation {PE} (r(t)Phi(x'))'+tilde c(t)Phi(x)=0, i.e., eqref{*} can be seen in the form (r(t)Phi(x')'+tilde c(t)Phi(x)+(c(t)-tilde c(t))Phi(x)=0. First we consider Hille-Wintner type comparison criteria and give a generalization of these kind of statements for {*} regarded as a perturbation. We formulate also immediate consequences for the case wh

Název v anglickém jazyce

Oscillation and asymptotic theory of half-linear differential equations

Popis výsledku anglicky

In this thesis we investigate oscillatory and asymptotic properties of solutions of the half-linear second order differential equation {*} (r(t)Phi(x'))'+c(t)Phi(x)=0 where Phi(x):=|x|^{p-1} sgn x, p>1, and r, c are continuous functions, r(t)>0. Thecentral idea which goes through the entire thesis is the concept of perturbations. We regard equation {*} as a perturbation of another half-linear equation in the same form to get some results for a class of half-linear equations for which the classicalapproach fails. We consider equation {*} as a perturbation of a general (nonoscillatory) two-term equation {PE} (r(t)Phi(x'))'+tilde c(t)Phi(x)=0, i.e., eqref{*} can be seen in the form (r(t)Phi(x')'+tilde c(t)Phi(x)+(c(t)-tilde c(t))Phi(x)=0. First we consider Hille-Wintner type comparison criteria and give a generalization of these kind of statements for {*} regarded as a perturbation. We formulate also immediate consequences for the case wh

Druh

O - Ostatní výsledky

CEP obor

BC - Teorie a systémy řízení

OECD FORD obor

—

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2007

Kód důvěrnosti údajů

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