Semi-positone boundary value problems

Abstract

This chapter establishes the existence of nonnegative solutions for the Dirichlet boundary value problem

$$ \{ _{y(0) = 0,y(1) = b \geqslant 0{\text{ }}or{\text{ }}y(1) = 0,y(0) = b \leqslant 0}^{y'' + \mu f(y) = 0,0 \leqslant t \leqslant 1} $$

(1.1)

and the mixed problem

$$ \{ _{y'(0) = 0,y(1) = b \geqslant 0{\text{ }}or{\text{ }}y'(1) = 0,y(1) = b \geqslant 0.}^{y'' + \mu f(y) = 0,0 \leqslant t \leqslant 1} $$

(1.2)