Positive pseudo-symmetric solutions for higher order differential equation boundary value problems with sign changing nonlinearities

Abstract

In this paper, a new fixed point theorem in cone is applied to obtain the existence of two positive pseudo-symmetric solution for the 2 n-order differential equation boundary value problem y ( 2 n ) ( t ) = f t , y , y ″ , … , y 2 ( n - 1 ) , 0 ⩽ t ⩽ 1 , y ( 2 i ) ( 0 ) = 0 , y ( 2 i ) ( 1 ) = y ( 2 i ) ( η ) , 0 ⩽ i ⩽ n - 1 , where f is allowed to change sign, η ∈ ( 0 , 1 ) .