Inequalities for Differential and Integral Equations
Academic Press, Nov 12, 1997 - Mathematics - 611 pages
Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course.
* Covers a variety of linear and nonlinear inequalities which find widespread applications in the theory of various classes of differential and integral equations
* Contains many inequalities which have only recently appeared in literature and cannot yet be found in other books
* Provides a valuable reference to engineers and graduate students
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application of Theorem applying Theorem Beesack Bihari Bondge and Pachpatte characteristic initial value completed by following connected subdomain continuous functions defined continuously differentiable functions Define a function defined for x e defined in Theorem defined on R+ desired inequality differential and integral differential inequality Dom(G ds dt dt ds easy to observe established by Pachpatte exists fact that u(t following theorem function z(t given by Pachpatte given in Theorem Gronwall h be nonnegative hyperbolic partial implies the estimate independent variables inequalities established inequality given initial value problem integrating with respect integro-differential equations inverse function keeping y fixed Lemma Let g(u Let u(x Let v(s Math monotonic nondecreasing nonlinear nonnegative constant nonnegative continuous functions obtain Pachpatte in press partial differential equations proof of Theorem required inequality results given Riemann function right-hand side subintervals t e R+ lying taken from Pachpatte ury(x Volterra integral equations Vz(t