Global structure of positive solutions for superlinear $2m$th-boundary value problems

Title:

Global structure of positive solutions for superlinear $2m$th-boundary value problems

Creator:

Ma, Ruyun and An, Yulian

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:463278e3-c4b9-430d-8ca2-e60b9afea169
uuid:463278e3-c4b9-430d-8ca2-e60b9afea169

Subject:

multiplicity results, Lidstone boundary value problem, eigenvalues, bifurcation methods, and positive solutions

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We consider boundary value problems for nonlinear $2m$th-order eigenvalue problem $$ \begin{aligned} (-1)^mu^{(2m)}(t)&=\lambda a(t)f(u(t)),\ \ \ \ \ 0<t<1, \\ u^{(2i)}(0)&=u^{(2i)}(1)=0,\ \ \ \ i=0,1,2,\cdots ,m-1 . \end{aligned} $$ where $a\in C([0,1], [0,\infty ))$ and $a(t_0)>0$ for some $t_0\in [0,1]$, $f\in C([0,\infty ),[0,\infty ))$ and $f(s)>0$ for $s>0$, and $f_0=\infty $, where $f_0=\lim _{s\rightarrow 0^+}f(s)/s$. We investigate the global structure of positive solutions by using Rabinowitz's global bifurcation theorem.

Language:

English

Rights:

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

Coverage:

161-172

Source:

Czechoslovak Mathematical Journal | 2010 Volume:60 | Number:1

Harvested from:

CDK

Metadata only:

false