The method of lower and upper solutions fornth-order periodic boundary value problems

[摘要] 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−1wherefis a Carathéodory function. We obtain sufficient conditions forfto guarantee the existence and approximation of solutions between a lower solutionαand an upper solutionβforn≥3with eitherα≤βorα≥β.For this, we study some maximum principles for the operatorLu≡u(n)+Mu. Furthermore, we obtain a generalization of the method of mixed monotonicity consideringfanduas vectorial functions.

[学科分类] 应用数学