Abstract
In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: − u″(t)=λ f( t,u( t)) for all t ∈ (0,1) subjecting to u(0)=0 and α u(η)= u(1), where η ∈ (0,1),α ∈[0,1), and λ is a positive parameter. The nonlinear term f(t,u) is nonnegative, and may be singular at t=0, t=1, and u=0. By the fixed point index theory and approximation method, we establish that there exists λ *∈(0,+∞], such that the above problem has at least two positive solutions for any λ ∈(0,λ *) under certain conditions on the nonlinear term f.
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