Differential Inequalities of Higher Order and the Asymptotic Solution of Nonlinear Boundary Value Problems

Abstract

Two differential inequality results of Nagumo on initial and boundary value problems for systems [Proc. Phys. Math. Soc. Japan, 19 (1937), pp. 861–866; 21 (1939), pp. 529–534] are combined to yield existence and comparison results on certain boundary value problems for nth order scalar nonlinear differential equations and their system analogues. This theory is then applied to several classes of singularly perturbed boundary value problems of higher order. Many examples are discussed in order to motivate the theory and indicate avenues of further study.