POSITIVE SOLUTIONS OF FOURTH-ORDER TWO-POINT BOUNDARY VALUE PROBLEMS

We study the existence of positive solutions of the equation f(x, y(x),y"(x)) =0 with either y(0)= y(1) =y"(0) = y"(1) =0 or y(0) = y'(1)=y"(0) = y"(1) = 0. We show the existence of at least one positive solution if f is either superlinear of sublinear by a simple application of a fixed point theorem In cones.