The Comprehensive Study of Differential Equations

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This research project is, as proposed, aimed to cover the fields of both ordinary differential equations and partial differential equaitons. The actual activities have been done at the general meeting on 20-22/12/1989 at Waseda University and at many other symposia and seminars organized for or related to this project. As a consequence of these activities a great number of significant and important results have been obtained in various branches of differential equations as listed below :(1) qualitative theory, such as the stability, oscillation, etc., of ordinary and functional differential equations in the real domain ;(2) analytic theory of ordinary and partial differential equations in the complex domain ;(3) theory for the special functions such as hypergeometric functions ;(4) theory of Hamiltonian systems ; and the control theory ;(5) the problem of existence, uniqueness, and the qualitative behaviors of solutions for linear partial differential equations (or systems) of hyperbolic, parabolic and elliptic types and linear Schrodinger equations ;(6) hypoellipticity ; theory of pseudo-differential operator ; scattering theory for wave equations ; theory of evolution equation ;(7) the problem of existence, uniqueness and asymptotic behaviors of positive global solutions, (non) bounded solution, blow-up solutions, viscosity solutions, etc., of nonlinear partial differential equations of hyperbolic, parabolic and elliptic types and of nonlinear Schrodinger equations ;(8) fundamental problems for nonlinear partial differential equations arising in fluid dynamics and other applied sciences, such as Navier-Stokes equations, Boltzmann equations, etc.