Kyungpook Mathematical Journal

  • 제46권1호
  • /
  • Pages.65-77
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  • 2006
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지

Oscillation of Second Order Nonlinear Elliptic Differential Equations

  • Xu, Zhiting (School of Mathematical Sciences, South China Normal University)
  • 투고 : 2004.07.05
  • 발행 : 2006.03.23
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초록

By using general means, some oscillation criteria for second order nonlinear elliptic differential equation with damping $$\sum_{i,j=1}^{N}D_i[a_{ij}(x)D_iy]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0$$ are obtained. These criteria are of a high degree of generality and extend the oscillation theorems for second order linear ordinary differential equations due to Kamenev, Philos and Wong.

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참고문헌

  1. D. Gilbarg, and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Spinger-Verlag, New York, 1983.
  2. I. V. Kamenev, An integral criterion for oscillation of linear differential equations, Math. Zamtki, 23(1978), 249-251 (In Russian).
  3. E. S. Noussair and C. A. Swanson, Oscillation of semilinear elliptic inequalities by Riccati transformation, Canad. J. Math., (4)32(1980), 908-923. https://doi.org/10.4153/CJM-1980-069-8
  4. Ch. G. Philos, Oscillation theorems for linear differential equations of second order, Arch. Math., 53(1989), 482-492. https://doi.org/10.1007/BF01324723
  5. C. A. Swanson, Semilinear second order elliptic oscillation, Canad. Math. Bull., (2)22(1979), 139-157. https://doi.org/10.4153/CMB-1979-021-0
  6. A. Wintner, A criterion of oscillatory stability, Quart. J. Appl. Math., 7(1949), 115-117. https://doi.org/10.1090/qam/28499
  7. J. S. W. Wong, On Kamenev-type oscillation theorems for second-order differential equations with damping, J. Math. Anal. Appl., 258(2001), 244-257. https://doi.org/10.1006/jmaa.2000.7376
  8. Z. T. Xu, Oscillation of second order elliptic partial differential equations with a "weakly integrally small" coefficient, J. Sys. and Math. Scis., (4)18(1998), 478-484 (In Chinese).
  9. Z. T. Xu, Riccati techniques and oscillation of semilinear elliptic equations, Chin. J. Contemp. Math., (4)24(2003), 329-340.
  10. Z. T. Xu, D. K. Ma and B. G. Jia, Oscillation theorems for elliptic equations of second order, Acta Math. Scientia (A), 24(2)(2004), 144-151 (In Chinese).
  11. B. G. Zhang, T. Zhao and B. S. Lalli, Oscillation criteria for nonlinear second order elliptic differential equations, Chin Ann of Math.(B), 9(17)(1996), 89-101.