Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 45, pp. 1-10.
Title: Positive solutions of a nonlinear higher order
boundary-value problem
Authors: John R. Graef (Univ. of Tennessee, Chattanooga, TN, USA)
Johnny Henderson (Baylor Univ., Waco, Texas, USA)
Bo Yang (Kennesaw State Univ., Kennesaw, GA, USA)
Abstract:
The authors consider the higher order boundary-value problem
$$\displaylines{
u^{(n)}(t)= q(t)f(u(t)), \quad 0 \leq t \leq 1, \cr
u^{(i-1)}(0) = u^{(n-2)}(p) = u^{(n-1)}(1)=0, \quad
1 \leq i \leq n-2,
}$$
where $n\ge 4$ is an integer, and $p\in(1/2,1)$ is a
constant. Sufficient conditions for the existence and nonexistence
of positive solutions of this problem are obtained. The main
results are illustrated with an example.
Submitted November 16, 2006. Published March 15, 2007.
Math Subject Classifications: 34B18.
Key Words: Existence and nonexistence of positive solutions;
Guo-Krasnosel'skii fixed point theorem;
higher order boundary value problem.