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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)

  1. "Bellman \paper The stabilityof solutions of linear differential equations \jour Duke Math. J.\vol 10 \yr 1943 \pages 643--647"
  2. "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"
  3. "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"
  4. "paper On certain new integral inequalities and their applications", 3, pp.1~8
  5. "paper Some integral inequalities for function of two variables", pp.1~13 (2003)
  6. "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"
  7. "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"
  8. "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"
  9. "V. Nemyckii and V. V. Stepanov \book Qualitative theory of differential equations$"
  10. "paper On some fundamental integral inequalities and their discrete analogues", 2, pp.1~13 (2001)

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