Singular perturbations of ordinary differential equations in Colombeau spaces

Marko Nedeljkov, Danijela Rajter

Abstract: In [3] and [4], for some class of nonlinear first order ordinary differential equations which contain delta distribution limits of solutions are computed when delta distribution is substituted by a delta net. We find a solution to the systems and equations of the above form in the sense of Colombeau generalized function spaces. Beside of the globally Lipschitz case in Theorem 2.1 whish is already solved in [1], the cases when a nonlinearity is not globally Lipschitz but with ``proper'' sign are covered by Theorem 3.2.

Keywords: ordinary differential equations, delta distribution, generalized solutions

Classification (MSC2000): 34A10; 46F10

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