Nonlinear triple-point problems with change of sign

In this paper, we study the existence of at least one or two positive solutions to the second-order triple-point nonlinear boundary value problem y″(x)+h(x)f(y(x))=0,x∈[a,b]y(a)=αy(η),y(b)=βy(η), where 0<α<β<10<α<β<1 and η∈(a,b)η∈(a,b). Here hh changes sign in ηη. As an application, we also give some examples to demonstrate our results.