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A new approximation scheme for first-order ordinary differential equations with non-negative right-hand sides

✍ Scribed by Rodrigo López Pouso

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
135 KB
Volume
54
Category
Article
ISSN
0362-546X

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✦ Synopsis

We prove an existence result for ÿrst-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 solutions. Our main result ensures the solvability of a type of discontinuous di erential equations that had not been previously considered.

📜 SIMILAR VOLUMES

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✍ Daniela Klose; Friedemann Schuricht 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 133 KB 👁 1 views

The paper studies differential equations of the form u (x) = f (x, u(x), λ(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 λ are stated.