On unbounded solutions of singular IVPs with ϕ-Laplacian
The result's identifiers
Result code in 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>
Alternative codes found
RIV/61989100:27600/17:10236896
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On unbounded solutions of singular IVPs with ϕ-Laplacian
Original language description
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>0,u(0)=u0∈[L0,L], u′(0)=0. Here, f is a continuous function with three roots ϕ(L0)<0<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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA14-06958S" target="_blank" >GA14-06958S: Singularities and impulses in boundary value problems for nonlinear ordinary differential equations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Qualitative Theory of Differential Equations
ISSN
1417-3875
e-ISSN
—
Volume of the periodical
2017
Issue of the periodical within the volume
80
Country of publishing house
HU - HUNGARY
Number of pages
26
Pages from-to
1-26
UT code for WoS article
000416388400001
EID of the result in the Scopus database
2-s2.0-85037660645