An Overview of the Lower and Upper Solutions Method with Nonlinear Boundary Value Conditions
نویسنده
چکیده
The first steps in the theory of lower and upper solutions have been given by Picard in 1890 1 for Partial Differential Equations and, three years after, in 2 for Ordinary Differential Equations. In both cases, the existence of a solution is guaranteed from a monotone iterative technique. Existence of solutions for Cauchy equations have been proved by Perron in 1915 3 . In 1927, Müller extended Perron’s results to initial value systems in 4 . Dragoni 5 introduces in 1931 the notion of the method of lower and upper solutions for ordinary differential equations with Dirichlet boundary value conditions. In particular, by assuming stronger conditions than nowadays, the author considers the second-order boundary value problem
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