scholarly journals Perturbations of local maxima and comparison principles for boundary-degenerate linear differential equations

2020 ◽  
Vol 373 (8) ◽  
pp. 5275-5332
Author(s):  
Paul M. N. Feehan
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Comparison Principles ◽  
Local Maxima ◽  
Linear Differential ◽  
Degenerate Linear

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.

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