BOUNDARY VALUE PROBLEMS VIA AN INTERMEDIATE VALUE THEOREM

Abstract

AbstractWe use an intermediate value theorem for quasi-monotone increasing functions to prove the existence of the smallest and the greatest solution of the Dirichlet problemu″ +f(t,u) = 0,u(0) = α,u(1) = β between lower and upper solutions, wheref:[0,1] ×E→Eis quasi-monotone increasing in its second variable with respect to a regular cone.