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Zbl 1097.35001
Lungu, Nicolaie
Qualitative problems in the theory of hyperbolic differential equations. (English)
[B] Cluj-Napoca: Digital Data Publishing. 105~p. (2006). ISBN 973-7768-19-1/pbk

Integral inequalities with explicit estimates play a very important role in the study of qualitative behavior of solutions of various types of differential equations. \par The present monograph deals with some results of the author and his co-workers related to the study of qualitative behavior of solutions of certain partial differential equations of hyperbolic type by operatorial method. The well known Gronwall-Wendroff type integral inequalities are discussed by the method of operatorial inequalities. The results on Picard and weakly Picard operators and the abstract Gronwall lemma are given. It also deals with the problems of existence, uniqueness, boundedness and comparison results. Differential and operatorial inequalities, Volterra integral equations in higher dimensions and applications to homogeneous economic growth models are also discussed. The monograph will be of interest to those, whose work involves the qualitative problems in the theory of hyperbolic differential equations.
[B. G. Pachpatte (Aurangabad)]

MSC 2000:: *35-02 Research monographs (partial differential equations)
35Lxx Hyperbolic equations and systems
35Bxx Qualitative properties of solutions of PDEs
35B05 General behavior of solutions of PDE
91B62 Dynamic economic models etc.
45D05 Volterra integral equations

Keywords: integral inequalities; Gronwall-Wendroff type integral inequalities; abstract Gronwall lemma

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