Existence theorems for the one-dimensional singular p-Laplacian equation with a nonlinear boundary condition

In this paper, general existence theorems are presented for the singular equation - ( ϕ p ( y ′ ) ) ′ = q ( t ) f ( t , y ) , 0 < t < 1 , y ( 0 ) = 0 , Ψ ( y ( 1 ) ) + y ′ ( 1 ) = 0 . Throughout, our nonlinearity is allowed to change sign. The singularity may occur at y = 0 , t = 0 and t = 1 . In addition, Ψ may be nonlinear.