A symmetric solution of a multipoint boundary value problem at resonance

We apply a coincidence degree theorem of Mawhin to show theexistence of at least one symmetric solution of the nonlinearsecond-order multipoint boundary value problem u″(t)=f(t,u(t),|u′(t)|),t∈(0,1), u(0)=∑i=1nμiu(ξi),u(1−t)=u(t),t∈[0,1], where 0<ξ1<ξ2<…<ξn≤1/2, ∑i=1nμi=1, f:[0,1]×ℝ2→ℝ with f(t,x,y)=f(1−t,x,y), (t,x,y)∈[0,1]×ℝ2, satisfying the Carathéodory conditions