The method of upper and lower solutions for a Lidstone boundary value problem

Title:

The method of upper and lower solutions for a Lidstone boundary value problem

Creator:

Guo, Yanping and Gao, Ying

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:abfe4ab7-5cf6-423c-94de-1794cbd04c69
uuid:abfe4ab7-5cf6-423c-94de-1794cbd04c69

Subject:

$n$-parameter eigenvalue problem, Lidstone boundary value problem, lower solution, and upper solution

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we develop the monotone method in the presence of upper and lower solutions for the $2$nd order Lidstone boundary value problem \[ u^{(2n)}(t)=f(t,u(t),u^{\prime \prime }(t),\dots ,u^{(2(n-1))}(t)),\quad 0<t<1, u^{(2i)}(0)=u^{(2i)}(1)=0,\quad 0\le i\le n-1, \] where $f\:[0,1]\times \mathbb{R}^{n}\rightarrow \mathbb{R}$ is continuous. We obtain sufficient conditions on $f$ to guarantee the existence of solutions between a lower solution and an upper solution for the higher order boundary value problem.

Language:

English

Rights:

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

Coverage:

639-652

Source:

Czechoslovak Mathematical Journal | 2005 Volume:55 | Number:3

Harvested from:

CDK

Metadata only:

false