Positive solutions for some 1-dimensional boundary value problems of Laplace-type

This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type subject to the following boundary condition: where ϕ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly. Supported by the NNSF of China(10371006) and Tianyuan Youth Grant of China(10626033).