Nonlinear second order periodic value problems with caratheodory functions

Abstract

The purpose of this paper is to study the periodic boundary value problem −u″ = f(t,u), u(O) = u(2π), u′(O) = u′(2π) when f satisfies Caratheodory conditions. We show that a generalized upper and lower solution method is still valid and develop monotone iterative technique for finding minimal and maximal solutions. Moreover, we show that the set of solutions between the (generalized) lower and upper solutions is a compact and convex set provided that f is decreasing in u for fixed t.

Keywords:

• Upper and lower solutions
• monotone iterative technique
• caratheodory function

AMS(MOS)::

• 34B15
• 34C25