ON THE SOLUTIONS OF THE LINEAR DIFFERENTIAL EQUATIONS OF·OPERATORS
AFAF RADY AHMED;
Abstract
In the field of Mikusinski's operatorst, we are led to differential equations which can not be solved in closed form . ( By a solution in closed form we mean a solution
expressed in terms of elementary functions, that is, polynomials, rational functions, exponential, logarithmic and trigonometric functions, etc., ............).
The theorems involving the equation
an(A.) x<•l (A.)+a._,(A.)x<•-'l (A.)+... +a 0 (A.)x(A.)=O,O:s;..l.
where:
a, (A.), i = 0, 1,..., n are independent on, are given by Drobbots and Mikusinski [6].
B. Stankovic [18], [19] considered equation (I) Where a, (A.) e C,(A.) and proved the existence and the uniqueness of the solution in c;p(A.).
J. Mikusinski [8], [9] Solved equation ( I ) when a,(A,) are polynomials of s with numerical coefficients. Also, when a,(A,) are constant operators, he found that the corresponding characteristic equation not always has n-solutions. In fact he gave only the following example:
expressed in terms of elementary functions, that is, polynomials, rational functions, exponential, logarithmic and trigonometric functions, etc., ............).
The theorems involving the equation
an(A.) x<•l (A.)+a._,(A.)x<•-'l (A.)+... +a 0 (A.)x(A.)=O,O:s;..l.
where:
a, (A.), i = 0, 1,..., n are independent on, are given by Drobbots and Mikusinski [6].
B. Stankovic [18], [19] considered equation (I) Where a, (A.) e C,(A.) and proved the existence and the uniqueness of the solution in c;p(A.).
J. Mikusinski [8], [9] Solved equation ( I ) when a,(A,) are polynomials of s with numerical coefficients. Also, when a,(A,) are constant operators, he found that the corresponding characteristic equation not always has n-solutions. In fact he gave only the following example:
Other data
| Title | ON THE SOLUTIONS OF THE LINEAR DIFFERENTIAL EQUATIONS OF·OPERATORS | Other Titles | عن حل المعادلات التفاضلية ذات المؤثرات | Authors | AFAF RADY AHMED | Issue Date | 1995 |
Attached Files
| File | Size | Format | |
|---|---|---|---|
| AFAF RADY AHMED.pdf | 1.4 MB | Adobe PDF | View/Open |
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