Existence Theory for the Equations (G′(y))′ = qf(t,y,y′) and (G′(y) − pH(y))′ = − p′H(y) + qf(t,y)

Existence results are reported for second-order problems of the form (G′(y))′ = qf(t, y, y′) and (G′(y) − pH(y))′ = − p′H(y) + qf(t, y) with y satisfying Dirichlet or mixed boundary data. A Bernstein-Nagumo theory and a theory based on Lp norms is presented.