Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 20, pp. 1-10.

Title: Positive solutions  for a class of nonresonant
       boundary-value problems

Author: Xuemei Zhang (North China Electric Power Univ., Beijing, China)

Abstract:
 This paper concerns the existence and  multiplicity of
 positive solutions to the nonresonant second-order
 boundary-value problem
 $$
 Lx=\lambda w(t)f(t,x).
 $$
 We are interested in the operator $Lx:=-x''+\rho qx$ when
 $w$ is in $L^{p}$ for  $1\leq p \leq +\infty$.
 Our arguments are based on fixed point theorems in a cone
 and Holder's inequality. The nonexistence of positive solutions
 is also studied.
 
Submitted November 28, 2006. Published January 27, 2007.
Math Subject Classifications: 34B15.
Key Words: Positive solution; fixed point theorem; 
           existence; complete continuity.