Abstract
Let E be the Haar pyramid
where b, M ∈ R<Stack><Subscript>+</Subscript><Superscript>n</Superscript></Stack>, b= (b 1,…, b n ), M = (M 1,…, M n ) and b − M a > 0. Write E 0=[−r 0, 0] × [−b, b] where r 0 ∈ R +, Ω = E × C(E 0 ∪ E, R) × R n and
Suppose that f: Ω → R and φ: E 0 → R are given functions. Consider the Cauchy problem
where D y z = (D y 1 z,…, D yn z). In this Chapter we consider classical solutions of problem (2.1), (2.2). We assume that the operator f satisfies the Volterra condition.
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© 1999 Springer Science+Business Media Dordrecht
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Kamont, Z. (1999). Existence of Solutions on the Haar Pyramid. In: Hyperbolic Functional Differential Inequalities and Applications. Mathematics and Its Applications, vol 486. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4635-7_2
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DOI: https://doi.org/10.1007/978-94-011-4635-7_2
Publisher Name: Springer, Dordrecht
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