A multi-point boundary value problem with two critical conditions Original Research Article

We apply a coincidence degree theorem due to Mawhin to show the existence of at least one solution of the nonlinear second order multi-point boundary value problem View the MathML sourceu″(t)=f(t,u(t),u′(t)),t∈(0,1), Turn MathJax on View the MathML sourceu′(0)=u′(η),∑i=1nαiu(ηi)=u(1), Turn MathJax on where 0<η≤10<η≤1, 0<ηi<10<ηi<1, i=1,…,ni=1,…,n, View the MathML source∑i=1nαi=∑i=1nαiηi=1, n≥2n≥2, and f:[0,1]×R2→Rf:[0,1]×R2→R satisfying the Carathéodory conditions. In our setting both boundary conditions are responsible for resonance.