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BOUNDEDNESS IN THE FUNCTIONAL NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS

구윤회
한국수학교육학회|2015.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제22권 제2호|pp. 101-112

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참고문헌

키워드

h-stabilityt∞-similarityfunctional differential systems.
주제분류수학

초록

Alexseev's formula generalizes the variation of constants formula and permits the study of a nonlinear perturbation of a system with certain stability properties. In this paper, we investigate bounds for solutions of the functional nonlinear perturbed differential systems using the two notion of h-stability and t∞- similarity.

Abstract

Alexseev's formula generalizes the variation of constants formula and permits the study of a nonlinear perturbation of a system with certain stability properties. In this paper, we investigate bounds for solutions of the functional nonlinear perturbed differential systems using the two notion of h-stability and t∞- similarity.

참고문헌 (16)

  1. V.M. Alekseev, "An estimate for the perturbations of the solutions of ordinary differential equations", Vestn. Mosk. Univ. Ser. I. Math. Mekh, 2, pp.28~36 (1961)
  2. S.K. Choi, "h¡stability for nonlinear perturbed systems", Ann. of Diff. Eqs, 11, pp.1~9 (1995)
  3. S.K. Choi, "h¡stability in differential systems", Bull. Inst. Math. Acad. Sinica, 21, pp.245~262 (1993)
  4. S.K. Choi, "h-stability of differential systems via t1-similarity", Bull. Korean. Math. Soc, 34, pp.371~383 (1997)
  5. S.K. Choi, "Lipschitz exponential asymptotic stability for non-linear functional systems", Dynamic Systems and Applications, 6, pp.397~410 (1997)
  6. S.K. Choi, "Lipschitz stability for nonlinear functional differen-tial systems", Far East J. Math. Sci(FJMS), 15, pp.689~708 (1999)
  7. R. Conti, "Sulla: t1-similitudine tra matricie l'equivalenza asintotica dei sistemi dif-ferenziali lineari", Rivista di Mat. Univ. Parma, 8, pp.43~47 (1957)
  8. 구윤회, "BOUNDEDNESS IN THE PERTURBED DIFFERENTIAL SYSTEMS", 순수 및 응용수학, 20(3), pp.223~232 (2013), 한국수학교육학회
  9. Y.H. Goo, "Boundedness in nonlinear functional perturbed differential systems"
  10. 구윤회, "BOUNDEDNESS IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS", 충청수학회지, 26(3), pp.605~613 (2013), 충청수학회
  11. 구윤회, "h-STABILITY OF THE NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS", 충청수학회지, 23(4), pp.827~834 (2010), 충청수학회
  12. G.A. Hewer, "Stability properties of the equation by t1-similarity", J. Math. Anal. Appl, 41, pp.336~344 (1973)
  13. V. Lakshmikantham, "Differential and Integral Inequalities: Theory and Applications" (1969), Academic Press
  14. B.G. Pachpatte, "On some retarded inequalities and applications", J. Ineq. Pure Appl. Math, 3, pp.1~7 (2002)
  15. M. Pinto, "Perturbations of asymptotically stable differential systems", Analysis, 4, pp.161~175 (1984)
  16. M. Pinto, "Stability of nonlinear differential systems", Applicable Analysis, 43, pp.1~20 (1992)

관련 논문AI추천

BOUNDEDNESS IN THE PERTURBED DIFFERENTIAL SYSTEMS구윤회한국수학교육학회 · 이론수학과 교직수학2013 · 제20권 제3호Boundedness in the nonlinear perturbed differential systems via t∞–similarity구윤회한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제2호h-STABILITY AND BOUNDEDNESS IN FUNCTIONAL PERTURBED DIFFERENTIAL SYSTEMS구윤회한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제2호Boundedness in Perturbed functional differential systems via $t_{\infty}$-similarity구윤회, 최상일강원경기수학회 · 한국수학논문집2015 · 제23권 제2호Boundedness in nonlinear perturbed differential systems via $t_{\infty}$-similarity구윤회, 임동만강원경기수학회 · 한국수학논문집2016 · 제24권 제4호BOUNDEDNESS IN NONLINEAR FUNCTIONAL DIFFERENTIAL SYSTEMS VIA t∞-SIMILARITY구윤회한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제3호

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