Forced Monotone Methods

Abstract

We consider a two point conjugate boundary value problem of the form ( ) ( ( ) ( )) ( ) ( ) where , - is continuous and and are real. The method of upper and lower solutions, coupled with monotone methods, is useful if is independent of If the conjugate conditions, ( ) ( ) are replaced by right focal conditions ( ) ( ) then the method of upper and lower solutions, coupled with monotone methods, is useful in the case that depends on and on In this talk, we construct a boundary value problem of the form ( ) ( ( ) ( )) ( ) ( ) ( ) which is equivalent to the original two point conjugate problem and obtain sufficient conditions on and on such that the method of upper and lower solutions, coupled with monotone methods, is useful.