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Singularly Perturbed Nonlinear Boundary‐Value Problems Whose Reduced Equations Have Singular Points
Author(s) -
Howes F. A.
Publication year - 1977
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1977572135
Subject(s) - mathematics , singular perturbation , boundary value problem , singular solution , mathematical analysis , nonlinear system , method of matched asymptotic expansions , singular point of a curve , differential equation , order (exchange) , variety (cybernetics) , asymptotic analysis , physics , statistics , finance , quantum mechanics , economics
Using results on implicit first‐order differential equations, the existence and the asymptotic behavior of solutions of singularly perturbed second‐order boundary‐value problems whose reduced equations have singular points are studied. The variety of possible nonuniform behavior is investigated by means of a stability analysis of the reduced solutions and is illustrated with several model problems which are canonical in terms of the first‐order singular‐point theory.