Nonuniform nonresonant singular Dirichlet boundary value problems for the one-dimensional pp-Laplacian with sign changing nonlinearity

Existence results are presented for the nonuniform nonresonant singular boundary value problem {[ϕ(u′)]′+f(t,u,u′)=0,for t∈(0,1),u(0)=u(1)=0, where ϕ(s)=|s|p−2s,p>1ϕ(s)=|s|p−2s,p>1. The singularity may appear at u=0,t=0u=0,t=0 or t=1t=1, and the function ff may change sign. The existence of solutions is obtained via an upper and lower solutions method.