On unbounded solutions of singular IVPs with ϕ-Laplacian

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F17%3A73582796" target="_blank" >RIV/61989592:15310/17:73582796 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27600/17:10236896

Výsledek na webu

<a href="https://www.math.u-szeged.hu/ejqtde/p5995.pdf" target="_blank" >https://www.math.u-szeged.hu/ejqtde/p5995.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14232/ejqtde.2017.1.80" target="_blank" >10.14232/ejqtde.2017.1.80</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On unbounded solutions of singular IVPs with ϕ-Laplacian

Popis výsledku v původním jazyce

The paper deals with a singular nonlinear initial value problem with a ϕ-Laplacian (p(t)ϕ(u′(t)))′+p(t)f(ϕ(u(t)))=0, t&gt;0,u(0)=u0∈[L0,L], u′(0)=0. Here, f is a continuous function with three roots ϕ(L0)&lt;0&lt;ϕ(L), ϕ:R→R is an increasing homeomorphism and function p is positive and increasing on (0,∞). The problem is singular in the sense that p(0)=0 and 1/p may not be integrable in a neighbourhood of the origin. The goal of this paper is to prove the existence of unbounded solutions. The investigation is held in two different ways according to the Lipschitz continuity of functions ϕ−1 and f. The case when those functions are not Lipschitz continuous is more involved that the opposite case and it is managed by means of the lower and upper functions method. In both cases, existence criteria for unbounded solutions are derived.

Název v anglickém jazyce

On unbounded solutions of singular IVPs with ϕ-Laplacian

Popis výsledku anglicky

The paper deals with a singular nonlinear initial value problem with a ϕ-Laplacian (p(t)ϕ(u′(t)))′+p(t)f(ϕ(u(t)))=0, t&gt;0,u(0)=u0∈[L0,L], u′(0)=0. Here, f is a continuous function with three roots ϕ(L0)&lt;0&lt;ϕ(L), ϕ:R→R is an increasing homeomorphism and function p is positive and increasing on (0,∞). The problem is singular in the sense that p(0)=0 and 1/p may not be integrable in a neighbourhood of the origin. The goal of this paper is to prove the existence of unbounded solutions. The investigation is held in two different ways according to the Lipschitz continuity of functions ϕ−1 and f. The case when those functions are not Lipschitz continuous is more involved that the opposite case and it is managed by means of the lower and upper functions method. In both cases, existence criteria for unbounded solutions are derived.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA14-06958S" target="_blank" >GA14-06958S: Singularity a impulsy v okrajových úlohách pro nelineární obyčejné diferenciální rovnice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Electronic Journal of Qualitative Theory of Differential Equations

ISSN

1417-3875

e-ISSN

—

Svazek periodika

2017

Číslo periodika v rámci svazku

80

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

26

Strana od-do

1-26

Kód UT WoS článku

000416388400001

EID výsledku v databázi Scopus

2-s2.0-85037660645