본문 바로가기
KERD
논문KCI 등재

Asymptotic Behavior of Solutions of Certain Nonlinear Differential and Integro-differential Equations

Said R. Grace|Sandra Pinelas
장전수학회 (Jangjeon Mathematical Society)|2010.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제13권 제2호|pp. 133-148|DOI 10.17777/pjms.2010.13.2.003

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

Integro-differential equationsAsymptotic behaviorDifferential equationsBoundedness
주제분류수학

초록

We establish several growth theorems for second order nonlinear differential and integro-differential equations. We also give necessary and suffcient conditions for solutions of second order non-linear differential equations to be bounded together with their frst derivatives and investigate its asymptotic behavior.

Abstract

We establish several growth theorems for second order nonlinear differential and integro-differential equations. We also give necessary and suffcient conditions for solutions of second order non-linear differential equations to be bounded together with their frst derivatives and investigate its asymptotic behavior.

참고문헌 (28)

  1. I. Bihari, "A generalization of a lemma of Bellman and its applications to uniqueness problems of differential equations", Acta. Math. Acad. Sci. Hungar., 1, pp.81~94 (1956)
  2. M. Cecchi, "On the dynamics of the generalized Emden-Fowler equations", Georgian Math. J, 7, pp.269~282 (2000)
  3. M. Cecchi, "On nonoscillatory solutions of differential equations with p-Laplacian", Adv. Math. Sci. Appl, 11, pp.419~436 (2001)
  4. M. Cecchi, "Integral conditions for nonoscillation of second order nonlinear differential equations", Nonlinear Anal., T.M.A., 64, pp.1278~1289 (2006)
  5. T. A. Chanturia, "On monotonic solutions of systems of nonlinear differential equations (Russian)", Annales Polon. Math, 37, pp.59~70 (1980)
  6. D. S. Cohen, "The asymptotic behavior of a class of nonlinear differential equations", Proc. Amer. Math. Soc., 18, pp.607~609 (1967)
  7. A. Constantin, "On the asymptotic behavior of second order nonlinear differential equations", Rend. Mat. Appl., 13, pp.627~634 (1993)
  8. T. G. Hallam, "Asymptotic integration of second order differential equations with integrable coefficients", Siam. J. Appl. Anal., 19, pp.430~439 (1970)
  9. G. H. Hardy, "Inequalities" (1988), Cambridge Univ. Press
  10. I. T. Kiguradze, "Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations" (1993), Kluwer Academic Publishers Group
  11. G. Kvinikadze, "On strongly increasing solutions of system of nonlinear ordinary differential equations", Trudy Inst. Prikl. Mat. I. Vekua, 37, pp.41~49 (1990)
  12. O. Lipovan, "On the asymptotic behavior of solutions to a class of second order nonlinear differential equations", Glasg. Math. J., 45 (2003)
  13. F. M. Meng, "A note on Tong paper: the asymptotic behavior of a class of nonlinear differential equations of second order", Proc. Amer. Math. Soc, 108, pp.383~386 (1990)
  14. M. Marini, "On the asymptotic behavior of the solutions of a class of second order differential equations", J. Differential Eqns., 28, pp.1~17 (1978)
  15. J. D. Mirzov, "Asymptotic properties of solutions of the systems of nonlinear nonautonomous ordinary differen-tial equations, (Russian), Maikop, Adygeja Publ. 1993", Folia Fac. Sci. Nat. Univ. Masaryk. Brun., Brno, Mathematica, 14 (1993)
  16. M. Mizukami, "Asymptotic behavior of solutions of a class of second order quasilinear ordinary differential equations", Hiroshima Math. J, 32, pp.51~78 (2002)
  17. R. A. Moore, "The behavior of solutions of a linear differential equations of second order", Pacific J. Math, 5, pp.154~165 (1955)
  18. O. G. Mustafa, "Global existence of solutions with prescribed asymptotic behavior for second order nonlinear differential equations", Nonlinear Anal., 51, pp.339~368 (2002)
  19. M. Naito, "Asymptotic behavior of solutions of second order differential equations with integrable coefficients", Trans. Amer. Math. Soc., 282, pp.577~588 (1984)
  20. B. G. Pachpatte, "On some integral inequalities similar to Bellman-Bihari inequalities", J. Math. Anal. Appl, 49, pp.794~802 (1975)
  21. Ch. G. Philos, "Asymptotic behavior of solutions of second order nonlinear ordinary differ-ential equations", Nonlinear Anal., 24, pp.81~90 (1995)
  22. Y. V. Rogovchenko, "On the asymptotic behavior of solutions for a class of second order nonlinear differential equations", Collect. Math., 49, pp.113~120 (1998)
  23. T. Ta, "Existence and asymptotic behavior of positive solutions of second order quasilinear differential equations", Adv. Math. Sci. Appl, 9, pp.907~938 (1999)
  24. J. Tong, "The asymptotic behavior of a class of nonlinear differential equations of second order", Proc. Amer. Math. Soc, 84, pp.235~236 (1982)
  25. W. F. Trench, "On the asymptotic behavior of solutions of second order linear differential equations", Proc. Amer. Math. Soc, 14, pp.12~14 (1963)
  26. P. Waltman, "On the asymptotic behavior of solutions of a nonlinear differential equation", Proc. Amer. Math. Soc, 15, pp.918~923 (1964)
  27. Z. Yin, "Monotone positive solutions of second order nonlinear differential equation", Nonlinear Anal., 54, pp.391~403 (2003)
  28. Z. Zhao, "Positive solutions of nonlinear second order ordinary differential equations", Proc. Amer. Math. Soc., 121, pp.465~469 (1994)

관련 논문AI추천

ASYMPTOTIC BEHAVIOR OF A CERTAIN SECOND-ORDER INTEGRO-DIFFERENTIAL EQUATION김영진한국수학교육학회 · 이론수학과 교직수학2017 · 제24권 제1호Oscillation and nonoscillation criteria for differential equations of second order김낙중강원경기수학회 · 한국수학논문집2011 · 제19권 제4호BOUNDS OF SOLUTIONS OF AN INTEGRO-DIFFERENTIAL EQUATION INVOLVING IMPULSES김영진한국수학교육학회 · 이론수학과 교직수학2017 · 제24권 제3호Oscillation theorems of solutions for some differential equationsRakJoong Kim대한수학회 · 대한수학회논문집2004 · 제19권 제3호Oscillatory and asymptotic behavior of second order nonlinear differential equations with dampingE. Tunc, O. Ozdemir장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2014 · 제17권 제4호OSCILLATORY BEHAVIOR OF SECOND-ORDER HALF-LINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH DAMPING TERML. Gao, Q. Zhang, S. Liu장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제4호

이 간행물의 다른 논문 (13건)

ON INDEX MATRICES Part 2: Intuitionistic fuzzy caseKrassimir T. Atanassovpp. 121-126HOCHSCHILD KERNEL FOR LOCALLY BOUNDED FINITE-DIMENSIONAL REPRESENTATIONS OF A CONNECTED REDUCTIVE LIE GROUPAlexander I. Shternpp. 127-132NOTE ON CARLITZ’S TYPE q-EULER NUMBERS AND POLYNOMIALS김태균, 김영희, 이병제pp. 149-155RELATIVE DEFECTS AND MULTIPLE COMMON ROOTS OF TWO MEROMORPHIC FUNCTIONSSUBHAS S.BHOOSNURMATH, HARINA P. WAGHAMOREpp. 157-172Research on Convergence Based on Problem Solving in Mathematics Teaching and Learning서종진, 김태균pp. 173-195
원문 보기