Ambrosetti-Prodi-type results for a third order multi-point boundary value problem

Abstract

The authors study the third order boundary value problem $$u^{\pp\p}=f(t,u)+\lm e(t),\quad t\in (0,1),$$ $$u(0)=u^{\p}(p)=\int_q^1w(s)u^{\pp}(s)ds=0.$$ Using the lower and upper solution method and fixed point index theory, some Ambrosetti-Prodi-type results are obtained for the above problem.