Positive Solutions of Quasilinear Boundary Value Problems

This paper deals with the existence of positive solutions for the boundary value problem p t.f u9..9qlp t.f t,u.s0; a-t-b u a.s0su b., where f is either f-superlinear or f-sublinear at ` and f t, 0.may be negative and p is a positive continuous function. The results extend several known results for semilinear equations. Our approach is based on fixed point theory for completely continuous operators which leave invariant a suitable cone in a Banach space of continuous functions.