Abstract: The existence of multiple positive solutions of differe ntial equation (φ(y′))′+g(t)f(t,y)=0 under nonlinear boundary value condi tion y(0)-B₀(y′(0))=y(1)+B1(y′(1))=0 is studied, where g is allowed to be singular at the end points of (0,1). The authors prove with the use of L eggett-Williams fixed-point theorem that the problem has at least three positi ve solutions. By further using the theorem, they show that more, even infinitely many positive solutions may be obtained.

Key words: boundary value problem, multiple positive solutions, fixed-point theorem