Mathematical Sciences: Oscillatory Behaviour in Asymmetric  Systems with Loading
{'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}
This project will emphasize mathematical research on                       nonlinear differential equations motivated by studies of large                  loading on asymmetric systems which result in highly oscillatory                behavior of solutions.  By asymmetric systems one understands                   those systems in which there is a restoring force which is                      asymptotically linear along rays issuing from equilibrium to                    infinity, but not linear at infinity.  The oscillatory behavior                 has been observed in partial differential equations of all types                as well as with periodic solutions of ordinary differential                     equations and Hamiltonian systems.  Recent work has led to new                  insights into nonlinear oscillations in suspension bridges, ships               and elevators.                                                                       One focus of the present work will be to develop a general                 theory of periodic solutions of systems of ordinary differential                equations.  Questions of primary interest concern the number of                 distinct solutions, the stability of solutions and the                          persistence of solutions under damping.  Work is also expected to               continue on computational approaches to Hamiltonian systems as                  well as on parabolic problems with nonlinearities which describe                diffusion systems.                                                                   Applications are expected to arise in areas already                        mentioned in addition to electronics, in the behavior of                        nonlinear capacitors.  Methods from nonlinear functional analysis               will be combined with computational tools and singularity theory                in seeking broad general principles in the context of asymmetric                systems.
{'FirstName': 'Patrick', 'LastName': 'McKenna', 'PI_MID_INIT': 'M', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Patrick M McKenna', 'EmailAddress': 'j.mckenna@uconn.edu', 'NSF_ID': '000330002', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Connecticut', 'CityName': 'STORRS', 'ZipCode': '062699018', 'PhoneNumber': '8604863622', 'StreetAddress': '438 WHITNEY RD EXTENSION UNIT 11', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Connecticut', 'StateCode': 'CT', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'CT02', 'ORG_UEI_NUM': 'WNTPS995QBM7', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CONNECTICUT', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8722532.xml'}