| Attributes | Values |
|---|
| rdf:type
| |
| Description
| - 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. The central 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 classical approach 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
- 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. The central 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 classical approach 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 (en)
- Předmětem zájmu této disertační práce jsou oscilační a asymptotické vlastnosti řešení pololineárních diferenciálních rovnic druhého řádu (r(t)\Phi(x'))'+c(t)\Phi(x)=0, {*} kde \Phi(x):=|x|^{p-1} \sgn x, p>1, a r, c jsou spojité funkce, r(t)>0. Hlavní myšlenka, která se vine celou prací, je koncept perturbací (poruch). Rovnici {*} považujeme za perturbaci jiné pololineární rovnice v témže tvaru, abychom tak získali výsledky pro některé pololineární rovnice, pro něž klasický přístup selhává. Uvažujeme rovnici {*} jako poruchu obecné (neoscilatorické) rovnice se dvěma členy {PE} (r(t)\Phi(x'))'+\tilde c(t)\Phi(x)=0, tj., na rovnici {*} se můžeme dívat ve tvaru (r(t)\Phi(x')'+\tilde c(t)\Phi(x)+(c(t)-\tilde c(t))\Phi(x)=0. Nejprve se zabýváme srovnávacími kritérii Hille-Wintnerova typu, které zobecníme za předpokladu, že se na rovnici {*} díváme jako na rovnici porušenou. Formujuleme též několik důsledků pro případ, kdy perturbovanou rovnicí {PE} je polo (cs)
|
| Title
| - Oscillation and asymptotic theory of half-linear differential equations
- Oscillation and asymptotic theory of half-linear differential equations (en)
- Oscilační a asymptotická teorie pololineárních diferenciálních rovnic (cs)
|
| skos:prefLabel
| - Oscillation and asymptotic theory of half-linear differential equations
- Oscillation and asymptotic theory of half-linear differential equations (en)
- Oscilační a asymptotická teorie pololineárních diferenciálních rovnic (cs)
|
| skos:notation
| - RIV/70883521:28140/07:63505887!RIV08-MSM-28140___
|
| http://linked.open...avai/riv/aktivita
| |
| http://linked.open...avai/riv/aktivity
| |
| http://linked.open...vai/riv/dodaniDat
| |
| http://linked.open...aciTvurceVysledku
| |
| http://linked.open.../riv/druhVysledku
| |
| http://linked.open...iv/duvernostUdaju
| |
| http://linked.open...titaPredkladatele
| |
| http://linked.open...dnocenehoVysledku
| |
| http://linked.open...ai/riv/idVysledku
| - RIV/70883521:28140/07:63505887
|
| http://linked.open...riv/jazykVysledku
| |
| http://linked.open.../riv/klicovaSlova
| - Half-linear differential equations; Riccati equation; half-linear Euler equation; half-linear Euler-Weber equation; principal solution; oscillation criteria; perturbation (en)
|
| http://linked.open.../riv/klicoveSlovo
| |
| http://linked.open...ontrolniKodProRIV
| |
| http://linked.open...in/vavai/riv/obor
| |
| http://linked.open...ichTvurcuVysledku
| |
| http://linked.open...cetTvurcuVysledku
| |
| http://linked.open...UplatneniVysledku
| |
| http://linked.open...iv/tvurceVysledku
| |
| http://localhost/t...ganizacniJednotka
| |
![[RDF Data]](/fct/images/sw-rdf-blue.png)
![[cxml]](/fct/images/cxml_doc.png)
![[csv]](/fct/images/csv_doc.png)
![[text]](/fct/images/ntriples_doc.png)
![[turtle]](/fct/images/n3turtle_doc.png)
![[ld+json]](/fct/images/jsonld_doc.png)
![[rdf+json]](/fct/images/json_doc.png)
![[rdf+xml]](/fct/images/xml_doc.png)
![[atom+xml]](/fct/images/atom_doc.png)
![[html]](/fct/images/html_doc.png)