Nonhomogeneous boundary value problems for some nonlinear equations with singular ϕ-Laplacian

Using Leray–Schauder degree theory we obtain various existence results for the quasilinear equation problems ( ϕ ( u ′ ) ) ′ = f ( t , u , u ′ ) submitted to nonhomogeneous Dirichlet or nonlinear Neumann–Steklov boundary conditions on [ 0 , T ] , when ϕ : ] − a , a [ → R is an increasing homeomorphism, ϕ ( 0 ) = 0 . We compare the results with the ones proved earlier in the homogeneous case.