Boundary Value Problems via an Intermediate Value Theorem

Abstract

Abstract. We use an intermediate value theorem for quasi-monotone increasing functions to prove the existence of the smallest and the greatest solution of the Dirichlet problem u + f (t, u) = 0, u(0) = α, u(1) = β between lower and upper solutions, where f : [0, 1] × E → E is quasi-monotone increasing in its second variable with respect to a regular cone.2000 Mathematics Subject Classification. 34B15, 34C12, 34G20.