Twin positive solutions for three-point boundary value problems of higher-order differential equations
The authors obtain some multiplicity results for the \(n\)th-order three-point boundary value problem \[ y^{(n)}(t)+f(t,y(t),\dots, y^{(n-2)}(t))=0,\quad t\in (0,1),\tag{1} \] \[ y^{(i)}(0)=0,\quad i=0,1,\dots,n-2,\qquad y^{(n-1)}(1)=\alpha y^{(n-1)}(\eta),\tag{2} \] with \(\alpha \in [0,1)\) and \(\eta\in (0,1)\). They use a fixed-point theorem, similar to the one given by \textit{R. I. Avery, C. Chyan} and \textit{J. Henderson} [Comput. Math. Appl. 42, No. 3--5, 695--704 (2001; Zbl 1006.34022)], to prove the existence of at least two positive solutions to (1)--(2).
scientific article; zbMATH DE number 2171570