Geodesic
On some boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 35 (1996) no. 1, pp. 103-119 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 34A30, 34B05, 46F10, 46F99 
@article{AUPO_1996_35_1_a10,
     author = {Lig\k{e}za, Jan},
     title = {On some boundary value problems for ordinary linear differential equations of second order in the {Colombeau} algebra},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {103--119},
     year = {1996},
     volume = {35},
     number = {1},
     mrnumber = {1485048},
     zbl = {0964.34010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_1996_35_1_a10/}
}
TY  - JOUR
AU  - Ligęza, Jan
TI  - On some boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 1996
SP  - 103
EP  - 119
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AUPO_1996_35_1_a10/
LA  - en
ID  - AUPO_1996_35_1_a10
ER  - 
%0 Journal Article
%A Ligęza, Jan
%T On some boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 1996
%P 103-119
%V 35
%N 1
%U http://geodesic.mathdoc.fr/item/AUPO_1996_35_1_a10/
%G en
%F AUPO_1996_35_1_a10
Ligęza, Jan. On some boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 35 (1996) no. 1, pp. 103-119. http://geodesic.mathdoc.fr/item/AUPO_1996_35_1_a10/

[1] Antosik P., Mikusiński J., Sikorski R.: Theory of distributions. The sequential approach. Amsterdam-Warsaw, 1973. | MR | Zbl

[2] Colombeau J. F.: Elementary introduction to new generalized functions. Amsterdam-New York-Oxford-North Holland, 1985. | MR | Zbl

[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. | MR | Zbl

[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)

[5] Deo S. G., Pandit S. G.: Differential systems involving impulses. Lecture Notes 954 (1982). | Zbl

[6] Doležal V.: Dynamics of linear systems. Praha, 1964. | MR

[7] Hildebrandt T. H.: On systems of linear differential Stieltjes integral equations. Illinois Jour. of Math. 3 (1959), 352-373. | MR

[8] Kurzweil J.: Generalized ordinary differential equations and continuous dependence on a parameter. Czech. Math. Jour. 7 (1957), 418-447. | MR | Zbl

[9] Kurzweil J.: Linear differential equations with distributions as coefficuints. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys. 7 (1959), 557-560. | MR

[10] Lasota A., Opial Z.: Sur les solutions périodiques des equations differentielles ordinaires. Ann. Polon. Math. 16 (1964), 69-94. | MR | Zbl

[11] Ligęza J.: Generalized solutions of ordinary linear differential equations in the Colombeau algebra. Math. Bohemica, 2 (1993), 123-146. | MR | Zbl

[12] Ligęza J.: Weak solutions of ordinary differential equations. Prace Naukowe U. Śl. w Katowicach, 842 (1986). | MR

[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. | MR | Zbl

[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

[15] Pfaff R.: Generalized systems of linear differential equations. Proc. of the Royal Soc. of Edingburgh, S. A. 89 (1981), 1-14. | MR | Zbl

[16] Pelant M., Tvrdý M.: Linear distributional differential equations in the space of regulated functions. Math. Bohemica, 4 (1993), 379-400. | MR

[17] Persson J.: The Cauchy system for linear distribution differential equations. Functial Ekvac. 30 (1987), 162-168.

[18] Schwabik Š., Tvrdý M., Vejvoda O.: Differential and integral equations. Praha, 1979. | MR

[19] Schwartz L.: Sur L’impossibilité de la multiplication des distributions. C. R. Acad. Sci. Paris, 239 (1954), 847-848. | MR | Zbl

[20] Wyderka Z.: Some problems of optimal control for linear systems with measures as coefficuints. Systems Science 5, 4 (1979), 425-431. | MR