Eigenvalue criteria for the existence of multiple positive solutions of high-order nonlinear BVPs

The existence of multiple positive solutions for the integral equation u(t)=∫01g(t,s)h(s)f(s,An−1u(s),…,A1u(s),u(s))ds is studied by using eigenvalue criteria. Using these results we obtain new results on the existence of multiple positive solutions for high-order nonlinear differential equations, subject to local and nonlocal boundary conditions.