Positive Solutions and Nonlinear Eigenvalue Problem of One-Dimensional p -Laplacian FDE

In this paper we are concerned with the nonlinear eigenvalue problem consisting of the functional differential equation with p -Laplacian operator, ( { p ( u '))' + u a ( t ) f ( t , u t ) = 0, { p ( s ) = | s | p m 2 s , p > 1, the initial condition, u ( s ) = } ( s ), m h s h 0, and the boundary condition, u (0) = 0 = u (1), where a ( t ) is allowed to be singular at the end points of (0, 1). Our results apply to more than just the sublinear and superlinear cases discussed in other references.