Mathematical Sciences: Critical Point Theory and            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}
Work will be done in the application of variational methods                to differential equations.  It will focus on three areas:                       critical point theory and Hamiltonian systems, on elliptic                      differential equations arising in curvature problems of                         differential geometry and on multiplicity questions for                         superlinear second order elliptic boundary value problems.                           Although superlinear equations have been studied for some                  time, certain results are only partially understood.  One of the                important ones is the existence of infinitely many solutions of                 the Dirichlet problem with null boundary values.  Efforts will be               made to determine some global reason applicable to all                          superlinear equations.  This will have to be achieved through a                 more abstract approach, possible using new complexification                     ideas.                                                                               Work on Hamiltonian systems will follow two directions.  The               first is to determine the degree of regularity of generalized                   solutions to Hamiltonian systems with singular potentials; the                  second is to continue studies on the Weinstein conjecture.  This                latter concerns periodic orbits on odd-dimensional compact                      manifolds.  It is believed that every contact vector-field has                  such an orbit if the first homology group of the manifold is                    zero.  Previous work on this conjecture has led to ideas of                     critical points at infinity and pseudo-orbits of contact forms.                 These, in turn, have produced partial solutions to the                          conjecture.                                                                          Work of a more geometric nature will center on the Kazdan -                Warner problem on spheres of dimension five or greater.  The                    fundamental question is one of deciding when a given function is                the curvature of a metric conformal to the standard one.                        Positive results for the three-sphere do not carry over to higher               dimensions.                                                                          In addition to making fundamental contributions to the                     fields of differential geometry and partial differential                        equations, this work can be applied to dynamical systems and                    potential theory.
[{'FirstName': 'Joseph', 'LastName': "D'Atri", 'PI_MID_INIT': 'E', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': "Joseph E D'Atri", 'EmailAddress': None, 'NSF_ID': '000165367', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}, {'FirstName': 'Abbas', 'LastName': 'Bahri', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Abbas Bahri', 'EmailAddress': 'abahri@math.rutgers.edu', 'NSF_ID': '000298455', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}]
{'Name': 'Rutgers University New Brunswick', 'CityName': 'NEW BRUNSWICK', 'ZipCode': '089018559', 'PhoneNumber': '8489320150', 'StreetAddress': '3 RUTGERS PLZ', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New Jersey', 'StateCode': 'NJ', 'CONGRESSDISTRICT': '12', 'CONGRESS_DISTRICT_ORG': 'NJ12', 'ORG_UEI_NUM': 'M1LVPE5GLSD9', 'ORG_LGL_BUS_NAME': 'RUTGERS, THE STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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