Mathematical Sciences: Asymptotic Solutions of Differential Equations
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
8821547                                                                         Sibuya                                                                               This project will continue work focusing on the properties                 of solutions of ordinary differential equations defined in the                  real and complex domain. There are four main areas under                        consideration. The first consists of studies on the asymptotic                  behavior of solutions of a first-order system of linear                         differential equations as the real independent variable                         increases indefinitely.  This work extends results in the                       textbook of Coddington and Levinson.  A second line of                          investigation will consider order linear differential equations                 of higher order in which the coefficients of the derivatives                    are given by holomorphic functions.  The object of this                         investigation will be to give a new interpretation in terms of                  the algebraic formalism of D-modules to the question whether                    the inhomogeneous equation can be solved in a sector of the                     complex plane.  General results on differential equations are                   to be derived as elementary consequences of the theory of                       injective modules.  Related work will also be done studying                     asymptotic solutions of mildly nonlinear systsms of equations                   of Gevrey type.  The difference in this effort will be the                      introduction of singular perturbations.  Solutions are expected                 to reflect the same growth properties as those from the                         unperturbed equations for small values of the parameter.  The                   final theme will treat the classical Stokes multipliers of                      Riemann's theory of hypergeometric equations.  The multipliers                  give invariants of equations.  In this context, parameters will                 be introduced into the equations and the properties of the                      multipliers will be studied as functions of the parameters.                     Some results of this type can be derived from the principal                     investigator's 1975 book.
{'FirstName': 'Yasutaka', 'LastName': 'Sibuya', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Yasutaka Sibuya', 'EmailAddress': None, 'NSF_ID': '000339278', 'StartDate': '06/15/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Minnesota-Twin Cities', 'CityName': 'MINNEAPOLIS', 'ZipCode': '554552009', 'PhoneNumber': '6126245599', 'StreetAddress': '200 OAK ST SE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Minnesota', 'StateCode': 'MN', 'CONGRESSDISTRICT': '05', 'CONGRESS_DISTRICT_ORG': 'MN05', 'ORG_UEI_NUM': 'KABJZBBJ4B54', 'ORG_LGL_BUS_NAME': 'REGENTS OF THE UNIVERSITY OF MINNESOTA', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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