On a two-point boundary value problem for second order singular equations

Title:

On a two-point boundary value problem for second order singular equations

Creator:

Lomtatidze, Alexander and Torres, P.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:eea04279-e08c-4b85-bb2d-76a9771b69c3
uuid:eea04279-e08c-4b85-bb2d-76a9771b69c3

Subject:

second order singular equation, two-point boundary value problem, and solvability

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The problem on the existence of a positive in the interval $\mathopen ]a,b\mathclose [$ solution of the boundary value problem \[ u^{\prime \prime }=f(t,u)+g(t,u)u^{\prime };\quad u(a+)=0, \quad u(b-)=0 \] is considered, where the functions $f$ and $g\:\mathopen ]a,b\mathclose [\times \mathopen ]0,+\infty \mathclose [ \rightarrow \mathbb R$ satisfy the local Carathéodory conditions. The possibility for the functions $f$ and $g$ to have singularities in the first argument (for $t=a$ and $t=b$) and in the phase variable (for $u=0$) is not excluded. Sufficient and, in some cases, necessary and sufficient conditions for the solvability of that problem are established.

Language:

English

Rights:

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

Coverage:

19-43

Source:

Czechoslovak Mathematical Journal | 2003 Volume:53 | Number:1

Harvested from:

CDK

Metadata only:

false