Annali di Matematica Pura ed Applicata

, Volume 175, Issue 1, pp 277–283 | Cite as

Some oscillation theorems for a class of quasilinear elliptic equations

  • Hiroyuki Usami
Article

Abstract

Oscillation criteria are obtained for quasilinear elliptic equations of the form (E)below. We are mainly interested in the case where the coefficient function oscillates near infinity. Generalized Riccati inequalities are employed to establish our results.

Keywords

Elliptic Equation Coefficient Function Quasilinear Elliptic Equation Oscillation Criterion Oscillation Theorem 

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References

  1. [1]
    À. Elbert,Oscillation and nonoscillation theorems for some nonlinear ordinary differential equation, Lecture Notes in Mathematics,964:Ordinary and Partial Differential Equations (1982), pp. 187–212.Google Scholar
  2. [2]
    À. Elbert -T. Kusano,Oscillation and nonoscillation theorems for a class of second order quasilinear differential equations, Acta Math. Hung.,56 (1990), pp. 325–336.Google Scholar
  3. [3]
    P. Hartman,Ordinary Differential Equations, 2nd ed, Birkhäuser, Boston (1982).Google Scholar
  4. [4]
    T. Kusano -A. Ogata -H. Usami,Oscillation theory for a class of second order quasilinear ordinary differential equations with application to partial differential equations, Japan. J. Math.,19 (1993), pp. 131–147.Google Scholar
  5. [5]
    T. Kusano -Y. Naito -A. Ogata,Strong oscillation and nonoscillation of quasilinear differential equations of second order, Differential Equations and Dynamical Systems,2 (1994), pp. 1–10.Google Scholar
  6. [6]
    T.Kusano - Y.Naito,Oscillation and nonoscillation criteria for second order quasilinear differential equation, Acta Math. Hung. (to appear).Google Scholar
  7. [7]
    E. S. Noussair -C. A. Swanson,Oscillation of semilinear Schrödinger equations and inequalities, Proc. Royal Soc. Edingburgh,75A (1976), pp. 67–81.Google Scholar
  8. [8]
    E. S. Noussair -C. A. Swanson,Oscillation theory for semilinear elliptic inequalities by Riccati trasformations, Canad. J. Math.,75 (1980), pp. 908–923.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1998

Authors and Affiliations

  • Hiroyuki Usami
    • 1
  1. 1.Department of Mathematics, Faculty of Integrated Arts and SciencesHiroshima UniversityHigashi-HiroshimaJapan

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