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

Abstract

The existence of multiple positive solutions for the integral equation u ( t ) = ∫ 0 1 g ( t , s ) h ( s ) f ( s , A n − 1 u ( s ) , … , A 1 u ( s ) , u ( s ) ) d s 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.