Steepest descent for general systems of linear differential equations in Hilbert space

1983 ◽  
pp. 390-406 ◽  
Author(s):  
J. W. Neuberger
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Steepest Descent ◽  
Linear Differential Equations ◽  
General Systems ◽  
Linear Differential

scholarly journals The behavior of solutions of non-linear differential equations in Hilbert space. I

1988 ◽  
Vol 11 (1) ◽  
pp. 143-165 ◽  
Author(s):  
Vladimir Schuchman
Keyword(s):  
Hilbert Space ◽  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Differential Equations ◽  
Linear Case ◽  
Cauchy Problems ◽  
The Cauchy Problem ◽  
Linear Differential ◽  
Degenerate Linear

This paper deals with the behavior of solutions of ordinary differential equations in a Hilbert Space. Under certain conditions, we obtain lower estimates or upper estimates (or both) for the norm of solutions of two kinds of equations. We also obtain results about the uniqueness and the quasi-uniqueness of the Cauchy problems of these equations. A method similar to that of Agmon-Nirenberg is used to study the uniqueness of the Cauchy problem for the non-degenerate linear case.

scholarly journals On behavior of solutions of non-linear differential equations in Hilbert space II

1988 ◽  
Vol 11 (2) ◽  
pp. 297-313
Author(s):  
Vladimir Schuchman
Keyword(s):  
Hilbert Space ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Linear Differential

This paper deals with the behavior of solutions of non-linear ordinary differntial equations in a Hilbert space with applications to non-linear partial differential equations.

scholarly journals An elementary inequality in function theory

1969 ◽  
Vol 10 (2) ◽  
pp. 162-168 ◽  
Author(s):  
W. N. Everitt
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Real Axis ◽  
Complex Plane ◽  
Analytic Functions ◽  
Function Theory ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Elementary Inequality ◽  
Adjoint Operators

In the theory of self-adjoint operators in Hilbert space and of formally self-adjoint linear differential equations there are many situations involving analytic functions on the complex plane whose singularities are confined to the real axis and where the growth of the function at such singular points is strictly limited.

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