scholarly journals A partial functional differential equation of Sobolev type

1983 ◽  
Vol 93 (2) ◽  
pp. 328-337 ◽  
Author(s):  
James H Lightbourne ◽  
Samuel M Rankin
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Sobolev Type ◽  
Functional Differential ◽  
Partial Functional Differential Equation

scholarly journals Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
T. E. Govindan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Local Lipschitz Condition ◽  
Functional Differential ◽  
Special Case ◽  
Partial Functional Differential Equation

This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation using a local Lipschitz condition. When the neutral term is zero and even in the deterministic special case, the result obtained here appears to be new. An example is included to illustrate the theory.

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