The upper and lower functions method for second order systems (Q5949165)

Summary: Two-point boundary value problems for \(m\)-dimensional second-order systems are considered. The method of upper and lower functions is applied to problems of the Dirichlet type and problems with nonlinear boundary conditions. The conditions on upper and lower functions are substantially relaxed comparing with the classical \(C^2\)-class, and properties of them are studied for systems with right-hand sides monotone in \(x\). Consequences for even-order differential equations with mixed monotonicities are given.