Degenerate Evolution Equations in Weighted Continuous Function Spaces, Markov Processes and the Black-Scholes Equation — Part I

2002 ◽  
Vol 42 (3-4) ◽  
pp. 193-211 ◽  
Author(s):  
Francesco Altomare ◽  
Antonio Attalienti
Keyword(s):  
Continuous Function ◽  
Markov Processes ◽  
Evolution Equations ◽  
Function Spaces ◽  
Black Scholes ◽  
Degenerate Evolution Equations

On injections and surjections of continuous function spaces

1973 ◽  
Vol 15 (3) ◽  
pp. 301-310 ◽  
Author(s):  
D. Amir ◽  
B. Arbel
Keyword(s):  
Continuous Function ◽  
Function Spaces

scholarly journals Density Problems in Sobolev’s Spaces on Time Scales

2021 ◽  
Vol 45 (02) ◽  
pp. 215-223
Author(s):  
AMINE BENAISSA CHERIF ◽  
FATIMA ZOHRA LADRANI
Keyword(s):  
Continuous Function ◽  
Time Scales ◽  
Time Scale ◽  
Function Spaces ◽  
First Order ◽  
Example Spaces

In this paper, we present a generalization of the density some of the functional spaces on the time scale, for example, spaces of rd-continuous function, spaces of Lebesgue Δ-integral and first-order Sobolev’s spaces.

scholarly journals A Class of Fractional Degenerate Evolution Equations with Delay

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1700
Author(s):  
Amar Debbouche ◽  
Vladimir E. Fedorov
Keyword(s):  
Unique Solvability ◽  
Evolution Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Systems Of Equations ◽  
Fractional Differential ◽  
Initial Boundary Value ◽  
Degenerate Type ◽  
Degenerate Evolution Equations ◽  
Equations With Delay

We establish a class of degenerate fractional differential equations involving delay arguments in Banach spaces. The system endowed by a given background and the generalized Showalter–Sidorov conditions which are natural for degenerate type equations. We prove the results of local unique solvability by using, mainly, the method of contraction mappings. The obtained theory via its abstract results is applied to the research of initial-boundary value problems for both Scott–Blair and modified Sobolev systems of equations with delays.

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