Inhomogeneous Abstract Differential Equations and Stabilization

2012 ◽  
pp. 123-141
Author(s):  
Birgit Jacob ◽  
Hans J. Zwart
Keyword(s):  
Differential Equations ◽  
Abstract Differential Equations

On recent developments in the theory of abstract differential equations with fractional derivatives

2010 ◽  
Vol 73 (10) ◽  
pp. 3462-3471 ◽  
Author(s):  
Eduardo Hernández ◽  
Donal O’Regan ◽  
Krishnan Balachandran
Keyword(s):  
Differential Equations ◽  
Fractional Derivatives ◽  
Abstract Differential Equations ◽  
Recent Developments

Existence of Solutions of Abstract Differential Equations in a Local Space

1973 ◽  
Vol 16 (2) ◽  
pp. 239-244
Author(s):  
M. A. Malik
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Differential Equations ◽  
Complex Plane ◽  
Hilbert Spaces ◽  
Scalar Product ◽  
Existence Of Solutions ◽  
Closed Linear Operator ◽  
Abstract Differential Equations ◽  
Local Space

Let H be a Hilbert space; ( , ) and | | represent the scalar product and the norm respectively in H. Let A be a closed linear operator with domain DA dense in H and A* be its adjoint with domain DA*. DA and DA*are also Hilbert spaces under their respective graph scalar product. R(λ; A*) denotes the resolvent of A*; complex plane. We write L = D — A, L* = D — A*; D = (l/i)(d/dt).

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