Pacific Journal of Mathematics

Nonoscillatory solutions of $(rx^{n})^{n}\pm f(t,\,x)x=0$.

Alan L. Edelson and Jerry D. Schuur

Article information

Pacific J. Math., Volume 109, Number 2 (1983), 313-325.

First available in Project Euclid: 8 December 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory
Secondary: 34C11: Growth, boundedness


Edelson, Alan L.; Schuur, Jerry D. Nonoscillatory solutions of $(rx^{n})^{n}\pm f(t,\,x)x=0$. Pacific J. Math. 109 (1983), no. 2, 313--325.

Export citation


  • [I] S. Ahmad, On the oscillation of a class of linear fourth order differential equations, Pacific J. Math., 34 (1970),289-299.
  • [2] G. Anichini and J. D. Schuur, A class of nonlinear ordinary differential equations with a 'characteristic equation', Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom.Phys., 26 (1978),787-790.
  • [3] S. N. Chow, D. R. Dunninger and J. D. Schuur, Oscillatory properties of solutions of n-thorder ordinary differential equations, Funkcial. Ekvac, 14 (1971), 191-196.
  • [4] R. Conti, Problems linearires pour les equations differentielles ordinalres,Math. Nachr.,23(1961), 161-178.
  • [5] C . C o r d u n e a n u , S u r les systems differentielsd e la f o r m e y ' = A ( x , y ) y -f b ( x , y), An.St. Univ. "Al. I. Cuza" Iasi (N.S.), 4 (1958),45-52.
  • [6] A. Edelson and K. Kreith, Nonlinear relationships between oscillation and asymptotic behaviour, Pacific J. Math., 102 (1982),29-39.
  • [7] G. J. Etgen and W. E. Taylor, Jr., The essential uniqueness of bounded nonoscillatory solutions of certain even order differential equations, Pacific J. Math., 68 (1977), 339-347.
  • [8] P. Hartman and A. Wintner, Linear differential and difference equations with mono- tone solutions, Amer. J. Math., 75 (1953),731-743.
  • [9] G. Jones, Oscillation properties ofy(n)+ py = 0, Proc. Amer. Math. So, 78 (1980), 239-244.
  • [10] A. G. Kartsatos, Nonzero solutions to boundary value problems for nonlinear systems, Pacific J. Math., 5 (1974), 425-433.
  • [II] K. Kreith, Extremal solutions for a class of nonlinear differential equations, Proc. Amer. Math. So,79 (1980), 415-421.
  • [12] T. Kusano and M. Naito, Nonlinear oscillation of fourth order differential equations, Canad. J. Math., XXVIII (1976),840-852.
  • [13] W. Leighton and Z. Nehari, On the oscillations of solutions of self-adjoint linear differential equations of the fourth order, Trans. Amer. Math. So, 89 (1958), 325-377.
  • [14] Z. Opial, Linearproblems for systems of nonlinear differential equations, J. Differential Equations, 3 (1967),580-594.
  • [15] J. D. Schuur, A class of ordinary differential equations which inherit linear-like asymptotic behavior, Nonlinear Analysis: Theory, Methods, and Applications, 3 (1979), 81-86.
  • [16] P. K. Wong, On a class of nonlinear fourth order differential equations, Ann. Mat. Pura E Appl., (4) 81 (1969), 331-346.