Optimal and Nonoptimal Gronwall Lemmas

Optimal and Nonoptimal Gronwall Lemmas

In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. A. Rus. This paper is also motivated by the fact that, in many i...

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Veröffentlicht in:Symmetry (Basel) 2020-10, Vol.12 (10), p.1728
Hauptverfasser: Marian, Daniela, Ciplea, Sorina Anamaria, Lungu, Nicolaie
Format: Artikel
Sprache:eng
Schlagworte:
abstract Gronwall lemma
Cauchy problems
Concrete
Inequalities
Inequality
Integral equations
optimal Bihari type inequality
optimal Gronwall lemma
optimal Riccati type inequality
Partial differential equations
Picard operators
Upper bounds
Wendorf type inequality
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Beschreibung
Zusammenfassung:In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. A. Rus. This paper is also motivated by the fact that, in many inequalities, the upper bound is not an optimal one.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym12101728