One-step methods of any order for ordinary differential equations with discontinuous right-hand sides
β Scribed by Reinhold Mannshardt
- Publisher
- Springer-Verlag
- Year
- 1978
- Tongue
- English
- Weight
- 993 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0029-599X
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π SIMILAR VOLUMES
Existence of extremal solutions for scalar initial value problems is investigated. We shall concentrate upon nonlinearities having constant sign, which lead to new existence results.
We prove an existence result for ΓΏrst-order ordinary di erential equations subject to initial conditions. Assuming that the nonlinear part of the equation is nonnegative, among some other technical hypotheses, we construct a new approximation scheme by means of which we obtain the existence of solut
The paper studies differential equations of the form u (x) = f (x, u(x), Ξ»(x)), u(x0 ) = u0 , where the righthand side is merely measurable in x. In particular sufficient conditions for the continuous and the differentiable dependence of solution u on the data and on the parameter Ξ» are stated.