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Journal: Annales Mathematicae Silesianae

Generalized periodic solutions of ordinary linear differential equations in the Colombeau algebra

Jan Ligęza

Language: EN | Published: 30-09-1997 | Abstract | pp. 67-87

It is shown that from the fact that the unique periodic solution of homogeneous system of equations is the trivial one it follows the existence of periodic solutions of nonhomogeneous systems of equations in the Colombeau algebra.

1997-09-30



Journal: Annales Mathematicae Silesianae

Remarks on generalized solutions of some ordinary nonlinear differential equations of second order in the Colombeau algebra

Jan Ligęza

Language: EN | Published: 30-09-1996 | Abstract | pp. 87-101

In this article some equations of second order are considered, whose nonlinearity satisfies a global Lipschitz condition. It is shown that the equations with additional conditions admit unique global solutions in the Colombeau algebra ????(ℝ¹).

1996-09-30