Existence and uniqueness of damped 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%2F16%3A33161446" target="_blank" >RIV/61989592:15310/16:33161446 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27600/16:86098462
Result on the web
<a href="http://www.math.u-szeged.hu/ejqtde/p5104.pdf" target="_blank" >http://www.math.u-szeged.hu/ejqtde/p5104.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14232/ejqtde.2016.1.121" target="_blank" >10.14232/ejqtde.2016.1.121</a>
Alternative languages
Result language
angličtina
Original language name
Existence and uniqueness of damped solutions of singular IVPs with ϕ-Laplacian
Original language description
We study analytical properties of a singular nonlinear ordinary differential equation with a ϕ-Laplacian. In particular we investigate solutions of the initial value problem (p(t)ϕ(u'(t)))'+ p(t)f(ϕ(u(t)))=0, u(0)=u_0 in [L_0,L], u'(0)=0 on the half-line [0,oo). Here, f is a continuous function with three zeros ϕ(L_0)<0<ϕ(L), function p is positive on (0,oo) and the problem is singular in the sense that p(0)=0 and 1/p(t) may not be integrable on [0,1]. The main goal of the paper is to prove the existence of damped solutions defined as solutions u satisfying sup {u(t), t in [0,oo)}<L. Moreover, we study the uniqueness of damped solutions. Since the standard approach based on the Lipschitz property is not applicable here in general, the problem is more challenging. We also discuss the uniqueness of other types of solutions.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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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
2016
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
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Volume of the periodical
2016
Issue of the periodical within the volume
121
Country of publishing house
HU - HUNGARY
Number of pages
28
Pages from-to
1-28
UT code for WoS article
000390898000001
EID of the result in the Scopus database
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