Asymptotic theory for a critical class of fourth-order differential equations
M. S. P. Eastham · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1982
Abstract A recently formulated asymptotic theory for differential equations with large coefficients that are like powers of the independent variable is developed here for fourth-order equations with general coefficients. In this general approach a critical case is identified that forms a borderline between situations where all solutions have asymptotically a certain exponential character in terms of the coefficients and where only two solutions have this character. The asymptotic forms of a fundamental set of solutions are obtained in the critical case.