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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&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.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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