A non-local existence theorem for systems of ordinary differential equations

1955 ◽  
Vol 4 (3) ◽  
pp. 301-308 ◽  
Author(s):  
K. L. Cooke
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Existence Theorem ◽  
Local Existence ◽  
Local Existence Theorem ◽  
Non Local

scholarly journals On some semilinear equations of Schrödinger type

2002 ◽  
Vol 90 (1) ◽  
pp. 139
Author(s):  
Rossella Agliardi ◽  
Daniela Mari
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Sobolev Spaces ◽  
Initial Value Problem ◽  
Local Existence ◽  
Weighted Sobolev Spaces ◽  
Initial Value ◽  
Semilinear Equations ◽  
Local Existence Theorem

We study the initial value problem for some semilinear pseudo-differential equations of the form $\partial _tu + i\ H(x,D_x)u = F(u,\nabla u)$. The assumptions we make on $H$ are trivially satisfied by $\Delta$, thus our equations generalize Schrdinger type equations. A local existence theorem is proved in some weighted Sobolev spaces.

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