| Title:
|
Boundary value problems for ordinary linear differential equations in the Colombeau algebra (English) |
| Author:
|
Ligęza, Jan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
95-112 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34A30 |
| MSC:
|
34B05 |
| MSC:
|
46F30 |
| idZBL:
|
Zbl 0956.34013 |
| idMR:
|
MR1767195 |
| . |
| Date available:
|
2009-01-29T15:55:55Z |
| Last updated:
|
2012-05-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120390 |
| . |
| Reference:
|
[1] Colombeau J. F.: Elementary introduction to new generalized functions.Amsterdam-New York-Oxford-North Holland, 1985. Zbl 0584.46024, MR 0808961 |
| Reference:
|
[2] Colombeau J. F.: Multiplication of distributions.Lecture Notes in Mathematics, 1532, 1992. Zbl 0815.35002, MR 1222643 |
| Reference:
|
[3] Denkowski Z.: On the boundary value problems for the ordinary differential equation of second order.Prace Matematyczne U. J. (Kraków) 12 (1968), 11-16. Zbl 0287.34014, MR 0224896 |
| Reference:
|
[4] Dłotko T.: Application of the notation of rotation of a vector field in the theory of differential equations and their applications.Prace Naukowe U. Śl. w Katowicach, 32 (1971), (in Polish) |
| Reference:
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[5] Deo S. G., Pandit S. G.: Differential systems involving impulses.Lecture Notes 954 (1982). Zbl 0539.34001 |
| Reference:
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[6] Doležal V.: Dynamics of linear systems.Praha, 1964. MR 0169744 |
| Reference:
|
[7] Egorov Y.: A theory of generalized functions.Uspehi Math. Nauk 455 (1990), 3-40 (in Russian). MR 1084986 |
| Reference:
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[8] Filippov A. F.: Differential equations with discontinuous right part.Moscow, 1985, (in Russian). |
| Reference:
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[9] Hildebrandt T. H.: On systems of linear differential Stieltjes integral equations.Illinois Jour. of Math. 3 (1959), 352-373. MR 0105600 |
| Reference:
|
[10] Kurzweil J.: Generalized ordinary differential equations.Czech. Math. J. 8 (1958), 360-389. Zbl 0102.07003, MR 0111878 |
| Reference:
|
[11] Lasota A., Opial Z.: Sur les solutions périodiques des equations differentielles ordinaires.Ann. Polon. Math. 16 (1964), 69-94. Zbl 0142.35303, MR 0170072 |
| Reference:
|
[12] Ligęza J.: Weak solutions of ordinary differential equations.Prace Naukowe U. Śl. w Katowicach, 842 (1986). MR 0868863 |
| Reference:
|
[13] Ligęza J.: Generalized solutions of boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra.Different aspect of differentiability, Dissertationes Mathematicae 340 (1995), 183-194. Zbl 0837.34026, MR 1342577 |
| Reference:
|
[14] Ligęza J.: Generalized solutions of ordinary linear differential equations in the Colombeau algebra.Math. Bohemica 2 (1993), 123-146. Zbl 0776.34046, MR 1223478 |
| Reference:
|
[15] Ligęza J.: Periodic solution of ordinary linear differential equations of second order in the Colombeau algebra.Different aspect of differentiability, Integral transforms and special functions 4, 1-2, 123-146. MR 1601207 |
| Reference:
|
[16] Ligęza J., Tvrdý M.: On systems of linear algebraic equations in the Colombeau algebra.Mathematica Bohemica 124, 1 (1999), 1-14. Zbl 0940.46022, MR 1687437 |
| Reference:
|
[17] Ligęza J.: Generalized periodic solutions of ordinary linear differential equations in the Columbeau algebra.Annales Mathematica Silesiana, Prace Naukowe U. Ś. w Katowicach, 11 (1997), 67-87. MR 1604875 |
| Reference:
|
[18] Ligęza J.: On some boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra.Acta Univ. Palacki. Olomuc., Fac. rer. nat. 35 (1996), 103-119. Zbl 0964.34010, MR 1485048 |
| Reference:
|
[19] Persson J.: The Cauchy system for linear distribution differential equations.Functial Ekvac. 30 (1987), 162-168. |
| Reference:
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[20] Pfaff R.: Generalized systems of linear differential equations.Proc. of the Royal Soc. of Edingburgh, S. A. 89 (1981), 1-14. Zbl 0475.34005, MR 0628123 |
| Reference:
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[21] Schwabik Š., Tvrdý M., Vejvoda O.: Differential and integral equations.Praha, 1979. MR 0542283 |
| Reference:
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[22] Wyderka Z.: Some problems of optimal control for linear systems with measures as coefficients.Systems Science 5, 4 (1979), 425-431. Zbl 0442.49002, MR 0572042 |
| . |
