1 research outputs found
Solvability of a higher-order multi-point boundary value problem at resonance
summary:Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point boundary value problem at resonance \displaylines { x^{(n)}(t)=f(t, x(t), x'(t),\cdots , x^{(n-1)}(t)),\quad t\in (0,1),\cr x(0)=\sum _{i=1}^{m}\alpha _{i}x(\xi _{i}),\quad x'(0)=\cdots =x^{(n-2)}(0)=0,\quad x^{(n-1)}(1)=\sum _{j=1}^{l}\beta _{j}x^{(n-1)}(\eta _{j}),\cr } where is a Carathéodory function, , , , and , , , . In this paper, two of the boundary value conditions are responsible for resonance