Address. National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, GREECE
Abstract. In this paper we use the method of upper and lower solutions to study multivalued Sturm--Liouville and periodic boundary value problems, with Caratheodory orientor field. We prove two existence theorems. One when the orientor field $F(t,x,y)$ is convex--valued and the other when $F(t,x,y)$ is nonconvex valued. Finally we show that the ``convex'' problem has extremal solutions in the order interval determined by an upper and a lower solution.
AMSclassification. 34B15, 34B24
Keywords. Upper solution, lower solution, order interval, usc multifunction, lsc multifunction, decomposable set, truncation map, penalty function, extremal solutions, Sturm--Liouville boundary conditions, periodic solutions