| Title:
|
On some boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra (English) |
| Author:
|
Ligęza, Jan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1996 |
| Pages:
|
103-119 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34A30 |
| MSC:
|
34B05 |
| MSC:
|
46F10 |
| MSC:
|
46F99 |
| idZBL:
|
Zbl 0964.34010 |
| idMR:
|
MR1485048 |
| . |
| Date available:
|
2009-01-29T15:49:26Z |
| Last updated:
|
2012-05-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120338 |
| . |
| Reference:
|
[1] Antosik P., Mikusiński J., Sikorski R.: Theory of distributions. The sequential approach.Amsterdam-Warsaw, 1973. Zbl 0267.46028, MR 0365130 |
| Reference:
|
[2] Colombeau J. F.: Elementary introduction to new generalized functions.Amsterdam-New York-Oxford-North Holland, 1985. Zbl 0584.46024, MR 0808961 |
| 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:
|
[5] Deo S. G., Pandit S. G.: Differential systems involving impulses.Lecture Notes 954 (1982). Zbl 0539.34001 |
| Reference:
|
[6] Doležal V.: Dynamics of linear systems.Praha, 1964. MR 0169744 |
| Reference:
|
[7] Hildebrandt T. H.: On systems of linear differential Stieltjes integral equations.Illinois Jour. of Math. 3 (1959), 352-373. MR 0105600 |
| Reference:
|
[8] Kurzweil J.: Generalized ordinary differential equations and continuous dependence on a parameter.Czech. Math. Jour. 7 (1957), 418-447. Zbl 0090.30002, MR 0111875 |
| Reference:
|
[9] Kurzweil J.: Linear differential equations with distributions as coefficuints.Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys. 7 (1959), 557-560. MR 0111887 |
| Reference:
|
[10] 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:
|
[11] 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:
|
[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.: Periodic solution of ordinary linear differential equations of second order in the Colombeau algebra.Proc. of the conference on different aspect of differentiability, Warsaw 1995, Integral transforms and special functions, to appear. MR 1601207 |
| Reference:
|
[15] 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:
|
[16] Pelant M., Tvrdý M.: Linear distributional differential equations in the space of regulated functions.Math. Bohemica, 4 (1993), 379-400. MR 1251883 |
| Reference:
|
[17] Persson J.: The Cauchy system for linear distribution differential equations.Functial Ekvac. 30 (1987), 162-168. |
| Reference:
|
[18] Schwabik Š., Tvrdý M., Vejvoda O.: Differential and integral equations.Praha, 1979. MR 0542283 |
| Reference:
|
[19] Schwartz L.: Sur L’impossibilité de la multiplication des distributions.C. R. Acad. Sci. Paris, 239 (1954), 847-848. Zbl 0056.10602, MR 0064324 |
| Reference:
|
[20] Wyderka Z.: Some problems of optimal control for linear systems with measures as coefficuints.Systems Science 5, 4 (1979), 425-431. MR 0572042 |
| . |
