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On some Gronwall type integral inequalities and their applications
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Abstract
The aim of the present paper is to establish somenonlinear integralinequalities in two independent variables which provide explicitbounds on unknown functions. The inequalities given here can beused as tools in the qualitative theory of certain partialdifferential equations.
참고문헌 (10)
- "Bellman \paper The stabilityof solutions of linear differential equations \jour Duke Math. J.\vol 10 \yr 1943 \pages 643--647"
- "Bihari \paper A generalization of a lemma of Bellman and its application touniqueness problems of differential equations \jour Acta Math. Acad. Sci. Hungar. \vol 7 \yr 1956 \pages 71--94"
- "S. Dragomir and N. M. Ionescu \paperOn nonlinear integral inequalities in two independent variables \jour Stud. Univ. Babe\c{s}-Bolyai Math. \vol 34 \yr1989 \pages 11--17"
- "paper On certain new integral inequalities and their applications", 3, pp.1~8
- "paper Some integral inequalities for function of two variables", pp.1~13 (2003)
- "H. Gronwall \paper Note on thederivatives with respect to a parameter of solutions of a system of differential equations \jour Ann. of Math. \vol 20 \yr 1919 \pages 292--296"
- "E. Langenhop \paper Bounds on thenorm of a solution of a general differential equation \jour Proc. Amer. Math. Soc. \vol 11 \yr 1960 \pages 795--799"
- "Mate and P. Neval \paper Sublinearperturbations of the differential equation $y^{ }=0$ and of the analogous difference equation \jour J. Differential Equations\vol 52 \yr 1984 \pages 234--257"
- "V. Nemyckii and V. V. Stepanov \book Qualitative theory of differential equations$"
- "paper On some fundamental integral inequalities and their discrete analogues", 2, pp.1~13 (2001)
관련 논문AI추천
On some Gronwall type inequalities for a system integral equation김병일대한수학회 · 대한수학회보2005 · 제42권 제4호New integral inequalities for nonlinear functions and their applicationsTae-In Kwon, Young-Ho Kim장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제16권 제1호On Some New Nonlinear Integral Inequalities of Gronwall- Bellman TypeAbdelwahab Abbas Ragab, Ahmed Abdel-moneim Eldeeb, Hassan mostafa El-Owaidy, Waleed mostafa kamal Abuelela경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제4호On certain new nonlinear retarded integral inequalities for functions in two variables and their applicationsJosip Pecaric, Qing-Hua Ma대한수학회 · 대한수학회지2008 · 제45권 제1호SOME RETARDED INTEGRAL INEQUALITIES AND THEIR APPLICATIONSYoung Jin Kim한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제2호On some new nonlinear retarded integral inequalities with iterated integrals and their applicationsJosip Pecaric, Qing-Hua Ma대한수학회 · 대한수학회지2008 · 제45권 제2호
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