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LIPSCHITZ AND ASYMPTOTIC STABILITY FOR PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS

구윤회
한국수학교육학회|2014.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제21권 제1호|pp. 11-21

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참고문헌

키워드

uniformly Lipschitz stabilityuniformly Lipschitz stability in variationexponentially asymptotic stabilityexponentially asymptotic stability in variation
주제분류수학

초록

The present paper is concerned with the notions of Lipschitz and as-ymptotic stability for perturbed nonlinear di®erential system knowing the corre-sponding stability of nonlinear di®erential system. We investigate Lipschitz andasymtotic stability for perturbed nonlinear di®erential systems. The main tool usedis integral inequalities of the Bihari-type, in special some consequences of an exten-sion of Bihari's result to Pinto and Pachpatte, and all that sort of things.

Abstract

The present paper is concerned with the notions of Lipschitz and as-ymptotic stability for perturbed nonlinear di®erential system knowing the corre-sponding stability of nonlinear di®erential system. We investigate Lipschitz andasymtotic stability for perturbed nonlinear di®erential systems. The main tool usedis integral inequalities of the Bihari-type, in special some consequences of an exten-sion of Bihari's result to Pinto and Pachpatte, and all that sort of things.

참고문헌 (18)

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  7. S.K. Choi, "Lipschitz stability for nonlinear functional differen-tial systems", Far East J. Math. Sci(FJMS)I, 5, pp.689~708 (1999)
  8. F.M. Dannan, "Lipschitz stability of nonlinear systems of differential sys-tems", J. Math. Anal. Appl, 113, pp.562~577 (1986)
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  10. 구윤회, "h-stability of the nonlinear perturbed differential systems via t_∞-similarity", 충청수학회지, 24(4), pp.695~702 (2011), 충청수학회
  11. 구윤회, "h¡STABILITY OF NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t1-SIMILARITY", 순수 및 응용수학, 19(2), pp.171~177 (2012), 한국수학교육학회[DOI]
  12. 구윤회, "BOUNDEDNESS IN THE PERTURBED DIFFERENTIAL SYSTEMS", 순수 및 응용수학, 20(3), pp.223~232 (2013), 한국수학교육학회
  13. 구윤회, "BOUNDEDNESS IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS", 충청수학회지, 26(3), pp.605~613 (2013), 충청수학회
  14. V. Lakshmikantham, "Differential and Integral Inequalities: Theory and Applications Vol.I" (1969), Academic Press
  15. B.G. Pachpatte, "A note on Gronwall-Bellman inequality", J. Math. Anal. Appl, 44, pp.758~762 (1973)
  16. M. Pinto, "Perturbations of asymptotically stable differential systems", Analysis, 4, pp.161~175 (1984)
  17. M. Pinto, "Integral inequalities of Bihari-type and applications", Funkcial. Ekvac, 33, pp.387~404 (1990)
  18. M. Pinto, "Variationally stable differential system", J. Math. Anal. Appl, 151, pp.254~260 (1990)

관련 논문AI추천

LIPSCHITZ AND ASYMPTOTIC STABILITY OF PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS구윤회, 최상일한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제1호UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS구윤회, Sang Il Choi한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제1호Lipschitz and asymptotic stability of nonlinear systems of perturbed differential equations구윤회, 최상일강원경기수학회 · 한국수학논문집2015 · 제23권 제1호On stability of nonlinear integro-differential systems with impulsive effect강보원, 구남집, 이현희대한수학회 · 대한수학회논문집2020 · 제35권 제3호h-STABILITY OF PERTURBED DIFFERENTIAL SYSTEMS구윤회한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제4호Uniformly Lipschitz stability and asymptotic property of perturbed functional differential systems구윤회, 임동만강원경기수학회 · 한국수학논문집2016 · 제24권 제1호

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