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On the Uniqueness and Boundedness of Solutions of Hyperbolic Differential Equations†

Published online by Cambridge University Press:  24 October 2008

V. Lakshmikantham
V. Lakshmikantham
Affiliation:
Osmania University, Hyderabad University of California, Los Angeles
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Extract

Consider a characteristic initial value problem of partial differential equations

where the functions E (x) and F (y) are real valued, uniformly Lipschitz continuous on 0 ≤ x ≤ a, 0 ≤ y ≤ b, respectively. Suppose f (x, y, u, p, q) is a real-valued and continuous function defined on 0 ≤ ≤ b. By a solution of (1), we mean a real-valued continuous function u (x, y), having partial derivatives ux (x, y), uy (x, y) and ux, y (x, y) in the domain 0 ≤ x ≤ a, 0 ≤ y ≤ b almost everywhere.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 4 , October 1962 , pp. 583 - 587
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

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