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Oscillation theorems for perturbed differential equations of second order

김낙중
대한수학회 (The Korean Mathematical Society)|2008.05|대한수학회보 (Bulletin of the KMS)|제45권 제2호|pp. 241-252

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참고문헌

키워드

comparison theoremRiccati transformoscillatory propertydelay differential equation
주제분류수학

초록

By means of a Riccati transform and averaging techniquesome oscillation criteria are established for perturbed nonlinear dieren-tial equations of second order (P₁) (p(t)x'(t))'+ q(t)|x((Φ(t))|α+1 sgn x(Φ(t)) + g(t,x(t)) = 0(P₂) and (P₃) satisfying the condition (H). A comparison theorem andexamples are given.

Abstract

By means of a Riccati transform and averaging techniquesome oscillation criteria are established for perturbed nonlinear dieren-tial equations of second order (P₁) (p(t)x'(t))'+ q(t)|x((Φ(t))|α+1 sgn x(Φ(t)) + g(t,x(t)) = 0(P₂) and (P₃) satisfying the condition (H). A comparison theorem andexamples are given.

참고문헌 (16)

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  4. M. Cecchi, "Comparison results for oscillation of nonlinear differential equations", Nonlinear Differential Equations and Applications, 6(2), pp.173~190 (1999)
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  7. S. R. Grace, "Oscillation theorems for second order nonlinear differential equations with damping", Mathematische Nachrichten, 141, pp.117~127 (1989)
  8. G. H. Hardy, "Inequalities" (1988), Cambridge University Press
  9. M. K. Kong, "Nonoscillation theorems for a second order sublinear ordinary differential equation", Proceedings of the American Mathematical Society, 87(3), pp.467~474 (1983)
  10. A. H. Nasr, "Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential", Proceedings of the American Mathematical Society, 126(1), pp.123~125 (1998)
  11. Ch. G. Philos, "Oscillation theorems for linear differential equations of second order", Archiv der Mathematik (Basel), 53(5), pp.482~492 (1989)
  12. Y. G. Sun, "A Note on Nasr and Wong papers", Journal of Mathematical Analysis and Applications, 286(1), pp.363~367 (2003)
  13. Y. G. Sun, "nonlinear differential equations with damping", Journal of Mathematical Analysis and Applications, 291(1), pp.341~351 (2004)
  14. J. S. W. Wong, "Oscillation criteria for second order nonlinear differential equations involving general means", Journal of Mathematical Analysis and Applications, 247(2), pp.489~505 (2000)
  15. J. S. W. Wong, "On Kamenev-type oscillation theorems for second-order differential equations with damping", Journal of Mathematical Analysis and Applications, 258(1), pp.244~257 (2001)
  16. C. C. Yeh, "Oscillation theorems for nonlinear second order differential equations with damped term", Proceedings of the American Mathematical Society, 84(3), pp.397~402 (1982)

관련 논문AI추천

Oscillation and nonoscillation criteria for differential equations of second order김낙중강원경기수학회 · 한국수학논문집2011 · 제19권 제4호Oscillation criteria of differential equations of second order김낙중강원경기수학회 · 한국수학논문집2011 · 제19권 제3호Oscillation Results for Second Order Nonlinear Differential Equation with Delay and Advanced ArgumentsEthiraju Thandapani, Murugesan Vijaya, Renu Rama, Srinivasan Selvarangam경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제1호Oscillation and nonoscillation theorems for nonlinear differential equations of second order김낙중, 김동일대한수학회 · 대한수학회지2007 · 제44권 제6호Oscillation criteria for second order differential inclusionsDonal O`Regan, Ravi P. Agarwal, Said R. Grace장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제16권 제1호OSCILLATORY BEHAVIOR OF SECOND-ORDER HALF-LINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH DAMPING TERML. Gao, Q. Zhang, S. Liu장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제4호

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