Asymptotics of a Second-Order Differential Equationwith a Small Parameter in the Case when the ReducedEquation Has Two Solutions

摘要

has a unique stable solution. (A detailed bibliography on this subject can be found in [1].) The situation issignificantly more complex if Eq. (2) has several solutions with intersecting graphs. For various problemsof this kind, the asymptotic behavior of solutions was investigated in some recent publications (e.g., see [2-4]). However, the only subjects in [2-4] were the limit of the solution as ￡ 0 and estimates for the dif-ference between the prelimit and limit solutions, while no complete analysis of the asymptotic expansionwas attempted.