We consider equations involving the one-dimensional p-Laplacianwith the Dirichlet boundary conditions. By using time map methods, we show how changes of the sign of f (·) lead to multiple positive solutions of the problem for sufficiently large λ.

In this paper, we establish existence of positive solutions of the nonlinear problems of one -dimensional p-Laplacian with nonlinear parameterwhere a : Ω → R is continuous and may change sign, λ > 0 is a parameter, f (λ, 0) > 0 for all λ > 0. By applying Leray-Schauder fixed point theorem we obtain the existence of positive solutions.