Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 89, pp. 1-12.

Title: Positive solutions of boundary-value problems for
       2m-order differential equations

Authors: Yuji Liu (Beijing Institute of Technology, China)
 Weigao Ge (Beijing Institute of Technology, China)

Abstract: 
 This article concerns the existence of positive
 solutions to the differential equation
 $$
 (-1)^m x^{(2m)}(t)=f(t,x(t),x'(t),\dots,x^{(m)}(t)),
 \quad  0<t<\pi,
 $$
 subject to boundary condition
 $$  x^{(2i)}(0)=x^{(2i)}(\pi)=0, $$
 or to the boundary condition
 $$  x^{(2i)}(0)=x^{(2i+1)}(\pi)=0,  $$
 for $i=0,1,\dots,m-1$.  Sufficient conditions for the
 existence of at least one positive solution of each
 boundary-value problem are established.
 Motivated by references [7,17,21], the  emphasis in
 this paper is that $f$ depends on all higher-order derivatives.
 
Submitted June 23, 2003. Published September 4, 2003.
Math Subject Classifications: 34B18, 34B15, 34B27
Key Words: Higher-order differential equation; boundary-value problem; 
           positive solution; fixed point theorem