The Method of Lower and Upper Solutions for nth – Order Periodic Boundary Value
نویسنده
چکیده
In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u(t) = f(t, u(t));u(a) − u(b) = λi ∈ R; i = 0, ..., n− 1. Where f is a Carathéodory function. We obtain sufficient conditions in f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n ≥ 3 either α ≤ β or α ≥ β. For this, we study some maximum principles for the operator Lu ≡ u + M u. Furthermore we obtain a generalization of the method of mixed monotony considering f and u vectorial functions.
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