The existence of countably many positive solutions for nonlinear singular m-point boundary value problems

In this paper, we study the existence of countably many positive solutions for nonlinear singular boundary value problem(@f(u^'))^'+a(t)f(u(t))=0,0R is an increasing homeomorphism and positive homomorphism and @f(0)=0,@x"i@?(0,1) with 0 [0,+~) and has countably many singularities in [0,12). We show that there exist countably many positive solutions by using the fixed-point index theory and a new fixed-point theorem in cones.

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