POSITIVE SOLUTIONS OF QUASI-LINEAR BOUNDARY-VALUE-PROBLEMS

This paper deals with the existence of positive solutions for the boun dary value problem (p(t)phi(u'))' + lambda p(t)f(t,u) = 0; a<t<b u(a)= 0=u(b), where f is either phi-superlinear or phi-sublinear at infinity 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 ope rators which leave invariant a suitable cone in a Banach space of cont inuous functions. (C) 1998 Academic Press.