We study the following strongly nonlinear differential equation: (a(t, x(t))(x (t))) = f(t, x(t), x (t)), a.e. in [0, T] subjected to various boundary conditions including, as particular cases, the classical Dirichlet, periodic, Neumann and Sturm-Liouville problems. We adopt the method of lower and upper solutions requiring a weak form of a Wintner-Nagumo growth condition. MS

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