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In this paper we develop the monotone method in the presence of lower and upper solutions for the problemu(n)(t)=f(t,u(t));u(i)(a)−u(i)(b)=λi∈ℝ,i=0,…,n−1where f is a Carathéodory function. We obtain sufficient conditions for f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n≥3 with either α≤β orα≥β

journal of applied mathematics and stochastic analysis

The method of lower and upper solutions for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$n$" id="E1"><mml:mi>n</mml:mi></mml:math> th-order periodic boundary value problems

The method of lower and upper solutions for n th-order periodic boundary value problems