Triple positive solutions and dependence on higher order derivatives

Abstract In this paper, we consider the Lidstone boundary value problem, y (2 m ) ( t ) =  f ( y ( t ),…, y (2 j ) ( t ),… y (2( m  − 1)) ( t )), 0 ≤  t  ≤ 1, y (2 i ) (0) = 0 =  y (2 i ) (1), 0 ≤  i  ≤  m  − 1, where (−1) m f  > 0. Growth conditions are imposed on f and inequalities involving an associated Green's function are employed which enable us to apply the Leggett–Williams Fixed Point Theorem to cones in ordered Banach spaces. This in turn yields the existence of at least three positive symmetric concave solutions. The emphasis here is that f depends on higher order derivatives.