본문 바로가기
KERD
논문KCI 등재

On some new nonlinear retarded integral inequalities with iterated integrals and their applications

Josip Pecaric|Qing-Hua Ma
대한수학회 (The Korean Mathematical Society)|2008.03|대한수학회지 (Journal of the KMS)|제45권 제2호|pp. 331-353

2

조회

0

다운로드

1

인용

0

참고문헌

키워드

Gronwall-like integral inequalitiesretardediterated integralspriori bound.
주제분류수학

초록

Some new nonlinear retarded integral inequalities of Gronwall- like type are established, which mainly generalized some results given by Cho, Dragomir and Kim (J. Korean Math. Soc. 43 (2006), No. 3, pp. 563–578) and can be used in the analysis of various problems in the theory of certain classes of differential equations and integral equations. Applications examples are also indicated.

Abstract

Some new nonlinear retarded integral inequalities of Gronwall- like type are established, which mainly generalized some results given by Cho, Dragomir and Kim (J. Korean Math. Soc. 43 (2006), No. 3, pp. 563–578) and can be used in the analysis of various problems in the theory of certain classes of differential equations and integral equations. Applications examples are also indicated.

참고문헌 (21)

  1. D. Baınov, "Integral Inequalities and Applications, Mathematics and its Applications (East European Series)", pp.57~ (1992), Academic Publishers Group
  2. R. Bellman, "Differential-difference Equations" (1963), Academic Press
  3. W. S. Cheung, "Some new nonlinear inequalities and applications to boundary value problems", NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 64(9), pp.2112~2128 (2006)
  4. W. S. Cheung, "Nonlinear retarded integral inequalities for functions in two independent variables", JOURNAL OF CONCRETE AND APPLICABLE MATHEMATICS, 2(2), pp.119~134 (2004)
  5. W. S. Cheung, "On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications", Journal of Inequalities and Applications, (4), pp.347~361 (2005)
  6. 조열제, "On some integral inequalities with iterated integrals", 대한수학회보, 43(3), pp.563~578 (2006), 대한수학회
  7. S. K. Choi, "W. N. Zhang, Nonlinear integral inequalities of Bihari-type without class H", MATHEMATICAL INEQUALITIES & APPLICATIONS, 8(4), pp.643~654 (2005)
  8. C. M. Dafermos, "The second law of thermodynamics and stability", Archive for Rational Mechanics and Analysis, 70(2), pp.167~179 (1979)
  9. S. S. Dragomir, "On certain new integral inequalities and their applications", Journal of Inequalities in Pure and Applied Mathematics, 4(3)통권 : 65, pp.8~ (2002)
  10. S. S. Dragomir, "Some integral inequalities for functions of two variables", Electronic Journal of Differential Equations, (10), pp.13~ (2003)
  11. H. Engler, "Global regular solutions for the dynamic antiplane shear problem in nonlinear viscoelasticity", Mathematische Zeitschrift, 202(2), pp.251~259 (1989)
  12. A. Haraux, "Nonlinear Evolution Equations—global behavior of solutions, Lecture Notes in Mathematics", pp.841~ (1981), Springer-Verlag
  13. V. Lakshmikantham, "Differential and Integral Inequalities: Theory and Applications. Vol. I, II, Mathematics in Science and Engineering, Vol. 55-I" (1969), Academic Press
  14. Q. H. Ma, "A more generalized Gronwall-like integral inequality with applications", International Journal of Mathematics and Mathematical Sciences, (15), pp.927~934 (2003)
  15. Q. H. Ma, "Some new nonlinear retarded integral inequalities and their applications", MATHEMATICAL INEQUALITIES & APPLICATIONS, 9(4), pp.617~632 (2006)
  16. Q. H. Ma, "On some new nonlinear delay integral inequalities", Journal of Mathematical Analysis and Applications, 252(2), pp.864~878 (2000)
  17. Q. H. Ma, "Some new Gronwall-Bellman-Bihari type integral inequalities with delay", Periodica Mathematica Hungarica, 44(2), pp.225~238 (2002)
  18. M. Medved, "Bihari type inequalities with multiple integral and delay", Periodica Mathematica Hungarica, 27(3), pp.207~212 (1993)
  19. F. W. Meng, "On some new integral inequalities and their applications", Applied Mathematics and Computation, 148(2), pp.381~392 (2004)
  20. D. S. Mitrinovic, "Inequalities Involving Functions and Their Integrals and Derivatives, Mathematics and its Applications (East European Series)", pp.53~ (1991), Kluwer Academic Publishers Group
  21. B. G. Pachpatte, "Inequalities for Differential and Integral Equations, Mathematics in Science and Engineering", pp.197~ (1998), Academic Press, Inc.

관련 논문AI추천

New integral inequalities for nonlinear functions and their applicationsTae-In Kwon, Young-Ho Kim장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제16권 제1호On 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 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 some Gronwall type integral inequalities and their applications김병일대한수학회 · 대한수학회보2004 · 제41권 제3호On Some Fractional Quadratic Integral InequalitiesAhmed M. A. El-Sayed, Hind H. G. Hashem경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제1호

이 간행물의 다른 논문 (19건)

Linear preservers of spanning column rank of matrix sums over semirings송석준pp. 301-312Schatten's theorem on absolute Schur algebrasPachara Chaisuriya, Jitti Rakbudpp. 313-329Complete moment convergence of moving average processes with dependent innovations김태성, 최용갑, 고미화pp. 355-365DIAGONAL LIFTS OF TENSOR FIELDS OF TYPE (1, 1) ON CROSS-SECTIONS IN TENSOR BUNDLES AND ITS APPLICATIONSArif Salimov, Aydin Gezerpp. 367-376Convergence of approximating paths to solutions of variational inequalities involving non-Lipschitzian mappings정종수, Daya Ram Sahupp. 377-392
원문 보기