Solutions of nonlinear differential equations. (English) Zbl 1196.34021
Summary: We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions. The solution of such an equation is a new generalized function. In this article we formulate necessary and sufficient conditions for when the solution of the given equation in the algebra of new generalized functions is associated with an ordinary function. Moreover, a class of all possible associated functions is described.
MSC:
| 34A99 | General theory for ordinary differential equations |
| 46F30 | Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) |
Keywords:
algebra of new generalized functions; differential equations with generalized coefficients; functions of finite variationReferences:
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