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The Solutions of a Model Nonlinear Singular Perturbation Problem Having A Continuous Locus of Singular Points
Author(s) -
Kedem Gershon,
Parter Seymour V.,
Steuerwalt Michael
Publication year - 1980
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/sapm1980632119
Subject(s) - mathematics , singular perturbation , multiplicity (mathematics) , limiting , bifurcation , nonlinear system , singular solution , mathematical analysis , locus (genetics) , boundary value problem , perturbation (astronomy) , singular value , bifurcation theory , pure mathematics , physics , eigenvalues and eigenvectors , mechanical engineering , biochemistry , chemistry , quantum mechanics , engineering , gene
Consider the boundary value problem εy″ =( y 2 − t 2 ) y′ , −1 ⩽ t ⩽0, y (−1) = A , y (0) = B . We discuss the multiplicity of solutions and their limiting behavior as ε →+0+ for certain choices of A and B . In particular, when A = 1, B = 0, a bifurcation analysis gives a detailed and fairly complete analysis. The interest here arises from the complexity of the set of "turning points."