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Multiple Solutions of Nonlinear Boundary‐Value Problems
Author(s) -
Rosenblat S.,
Szeto R.
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/sapm198063299
Subject(s) - boundary value problem , mathematics , nonlinear system , mathematical analysis , boundary (topology) , class (philosophy) , zero (linguistics) , physics , computer science , linguistics , philosophy , quantum mechanics , artificial intelligence
A class of nonlinear boundary‐value problems containing a parameter is studied analytically and numerically. It is shown that under certain circumstances there are two families of solutions when the parameter tends to zero; one family comprises small solutions and is obtained by regular perturbations, while the other family comprises finite solutions incorporating boundary and interior layers. It is shown by numerical integration that the two families are smooth continuations of each other when the parameter passes through finite values.