Eigenvalues of a general class of boundary value problem with derivative-dependent nonlinearity

We consider a general class of boundary value problem (BVP) comprising the differential equationy(m)(t)=λFt,y(t),y′(t),y″(t),…,y(q)(t),t∈(0,1)where 1⩽q⩽m-1 and λ>0, together with multi-point boundary conditionsy(0)=y′(0)=y″(0)=⋯=y(q-1)(0)=0,Aiy(q)(tj),y(q+1)(tj),…,y(m-1)(tj);0⩽j⩽r=0,1⩽i⩽m-qwhere 0=t0