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Applications of Linear Multi-Dimensional Integral and Difference Inequalities

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Integral and Discrete Inequalities and Their Applications

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Abstract

In this section, we shall use Theorems 5.1.1 and 5.1.10 and Corollaries 5.1.2 and 5.1.4 to study nonlinear vector hyperbolic partial differential equations.

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Bibliography

  1. O. Akinyele, On Gronwall-Bellman-Bihari-type integral inequalities in several variables with retardation. J. Math. Anal. Appl. 104 (1), 1–26 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Asirov, Ja. D. Mamedov, Investigation of solutions of nonlinear Volterra-Fredholm operator equations. Dokl. Akad. Nauk SSSR, 229, 982–986 (1976)

    Google Scholar 

  3. D. Bainov, P. Simeonov, Integral Inequalities and Applications (Kluwer Academic Publishers, Dordrecht, 1992)

    Book  MATH  Google Scholar 

  4. B.K. Bondge, Some contributions to integral inequalities. Ph.D. thesis, Marathwada University, India, 1979

    Google Scholar 

  5. B.K. Bondge, B.G. Pachpatte, On nonlinear integral inequalities of the Wendroff’s type. J. Math. Anal. Appl. 70 (1), 161–169 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  6. B.K. Bondge, B.G. Pachpatte, W. Walter, On generalized Wendroff type inequalities and their applications. Nonlinear Anal. 4, 491–495 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  7. E.T. Copson, On the Riemann-Green function. Arch. Ration. Mech. Anal. 1, 324–248 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Corduneanu, A note on Gronwall inequality in two independent variables. J. Integr. Equ. 4, 271–276 (1982)

    MathSciNet  MATH  Google Scholar 

  9. S.K. Ghoshal, M.A. Masood, Generalized Gronwall’s inequality and its applications to non-self-adjoint linear and nonlinear hyperbolic partial differential equations, to establish their uniqueness, continuous dependence and comparison theorems. Indian J. Pure Appl. Math. 5, 297–310 (1974)

    MathSciNet  MATH  Google Scholar 

  10. L. Hacia, On solving Volterra-Fredholm integral equations. Fasc. Math. 13, 21–30 (1981)

    MathSciNet  MATH  Google Scholar 

  11. D.Y. Kasture, S.G. Deo, Inequalities of Gronwall type in two independent variables. J. Math. Anal. Appl. 58, 361–372 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  12. R.K. Miller, J.A. Nohel, J.S.W. Wong, A stability theorem for nonlinear mixed integral equations. J. Math. Anal. Appl. 25, 446–449 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  13. B.G. Pachpatte, On some new integral and integrodifferential inequalities in two independent variables and their applications. J. Differ. Equ. 33, 249–272 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  14. B.G. Pachpatte, On the existence and uniqueness of solutions of Volterra-Fredholm integral equations. Math. Semin. Notes 10, 733–742 (1982)

    Google Scholar 

  15. B.G. Pachpatte, Inequalities for Differential and Integral Equations (Academic, New York, 1998)

    MATH  Google Scholar 

  16. B.G. Pachpatte, On some fundamental integral inequalities and their discrete analogues. J. Inequal. Pure Appl. Math. 2 (2), 3–31, Art.15 (2001)

    Google Scholar 

  17. B.G. Pachpatte, Explicit bounds on certain integral inequalities. J. Math. Anal. Appl. 267, 48–61 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  18. B.G. Pachpatte, On some retarded integral inequalities and applications. J. Inequal. Pure Appl. Math. 3, Art.18 (2002)

    Google Scholar 

  19. B.G. Pachpatte, Inequalities applicable to certain partial differential equations. J. Inequal. Pure Appl. Math. 5 (2), Article 27 (2004)

    Google Scholar 

  20. B.G. Pachpatte, S.M. Singare, Discrete generalised Gronwall inequalities in three independent variables. Pac. J. Math. 82, 197–210 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  21. A.M. Samoilenko, N. Perestyuk, Differential Equations with Impulse Effect (Visha Shkola, Kyiv, 1987) (in Russian)

    Google Scholar 

  22. S.M. Singare, Some contributions to finite difference inequalities. Ph.D. thesis, Marathwada University, India, 1979

    Google Scholar 

  23. D.R. Snow, A two independent variable Gronwall-type inequality, in Inequalities, III, Proceedings of the Third Symposium on Inequalities, Held at the University of California, 1969 (Academic, New York, 1971), pp. 330–340

    Google Scholar 

  24. E.H. Yang, On the most general form of Bellman type linear inequalities involving multiple-fold integral functionals. J. Math. Anal. Appl. 103, 184–197 (1984)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics College of Science, Donghua University, Shanghai, China

    Yuming Qin

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  1. Yuming Qin
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Qin, Y. (2016). Applications of Linear Multi-Dimensional Integral and Difference Inequalities. In: Integral and Discrete Inequalities and Their Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-33301-4_8

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