A unifying maximum principle for conjugate boundary value problems (Q2757091)

The author gives a maximum principle for the \(n\)th-order linear operator NEWLINE\[NEWLINEL x(t) \equiv x^{(n)}(t) + p_1(t) x^{(n-1)}(t) + \cdots + p_n(t) x(t)NEWLINE\]NEWLINE with \(x\) satisfying the boundary value conditions NEWLINE\[NEWLINEx^{(j)}(a_i) =0, \quad 1 \leq i \leq n,\;0 \leq j \leq k_i-1.NEWLINE\]NEWLINE Here, \(a_1 < \ldots < a_m\) and \(k_1, \ldots,k_m\) are positive integers such that \(2 \leq m \leq \sum_{i=1}^m{k_i}=n\), moreover, \(p_1, \ldots,p_n\) are given continuous functions in \([a_1,a_m]\). NEWLINENEWLINENEWLINESuch maximum principle includes, as a particular case, some previous results given by different authors, and it is applied to deduce the existence of solutions to some nonlinear multipoint boundary value problems.