Existence of positive solutions for singular four-point boundary value problem with a $p$-Laplacian

Title:

Existence of positive solutions for singular four-point boundary value problem with a $p$-Laplacian

Creator:

Miao, Chunmei, Zhao, Junfang, and Ge, Weigao

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:0ab0245f-66b9-4292-b449-b7bd5c1f1ba1
uuid:0ab0245f-66b9-4292-b449-b7bd5c1f1ba1

Subject:

singular, four-point, positive solution, and $p$-Laplacian

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we deal with the four-point singular boundary value problem $$ \begin {cases} (\phi _p(u'(t)))'+q(t)f(t,u(t),u'(t))=0,& t\in (0,1),\\ u'(0)-\alpha u(\xi )=0, \quad u'(1)+\beta u(\eta )=0, \end {cases} $$ where $\phi _p(s)=|s|^{p-2}s$, $p>1$, $0<\xi <\eta <1$, $\alpha ,\beta >0$, $q\in C[0,1]$, $q(t)>0$, $t\in (0,1)$, and $f\in C([0,1]\times (0,+\infty )\times \mathbb R,(0,+\infty ))$ may be singular at $u = 0$. By using the well-known theory of the Leray-Schauder degree, sufficient conditions are given for the existence of positive solutions.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

957-973

Source:

Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:4

Harvested from:

CDK

Metadata only:

false