Neumann and periodic boundary-value problems for quasilinear ordinary differential equations with a nonlinearity in the derivative

We present sufficient conditions for the existence of solutions to Neumann and periodic boundary-value problems for some class of quasilinear ordinary differential equations. We also show that this condition is necessary for certain nonlinearities. Our results involve the p-Laplacian, the mean-curvature operator and nonlinearities blowing up.