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.