Rocky Mountain Journal of Mathematics

Conjugacy Criteria for Second Order Differential Equations

Ondřej Došlý

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Rocky Mountain J. Math., Volume 23, Number 3 (1993), 849-861.

First available in Project Euclid: 5 June 2007

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Conjugate points conjugacy criteria disconjugacy principal solution


Došlý, Ondřej. Conjugacy Criteria for Second Order Differential Equations. Rocky Mountain J. Math. 23 (1993), no. 3, 849--861. doi:10.1216/rmjm/1181072527.

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  • C.D. Ahlbrandt, D.B. Hinton and R.T. Lewis, The effect of variable change on oscillation and disconjugacy criteria with applications to spectral and asymptotic theory, J. Math. Anal. Appl. 81 (1981), 234-277.
  • O. Boruvka, Lineare Differentialtransformationen 2. Ordnung, VEB, Deutscher Verlag der Wissenschaften, Berlin, 1971.
  • O. Došlý, On the existence of conjugate points for linear differential systems, Math. Slovaca 40 (1990), 87-99.
  • --------, Existence of conjugate points for self-adjoint linear differential equations, Proc. Roy. Soc. Edinburgh Sect. A 113 (1989), 73-85.
  • --------, On some problems in oscillation theory of self-adjoint linear differential equations, Math. Slovaca 41 (1991), 101-111.
  • P. Hartman, Ordinary differential equations, John Wiley, New York, 1964.
  • V. Komkov, A technique for detection of oscillation of second order ordinary differential equations, Pacific J. Math. 42 (1972), 105-115.
  • J. Krbila, The existence and unboundedness of the first hyperbolic phase of nonoscillatory differential equation $y^\pp\!+\!q(x)y\!=\!0$, Sborní k prací VŠD a V\' UD Žilina 25 (1969), 5-11 (in Czech).
  • E. Müller-Pfeiffer, Existence of conjugate points for second and fourth order differential equations, Proc. Roy. Soc. Edinburgh Sect. A 89 (1981), 281-291.
  • --------, Nodal domains of one- or two-dimensional elliptic differential equations, Z. Anal. Anwendungen 7 (1988), 135-139.
  • M. Ráb, Kriterien für die Oszillation der Lösungen der Differentialgleichung $(p(x)y^\p)^\p+q(x)y=0$, Čas. P\v est. Mat. 34 (1959), 335-370.
  • W.T. Reid, Sturmian theory for ordinary differential equations, Springer-Verlag, New York, Berlin, Heidelberg, 1980.
  • U.-W. Schminke, On the lower spectrum of Schrödinger operator, Arch. Rational Mech. Anal. 75 (1981), 147-155.
  • C.A. Swanson, Comparison and oscillation theory of linear differential equations, Academic Press, New York, 1968.
  • F.J. Tipler, General relativity and conjugate differential equations, J. Differential Equations 30 (1978), 165-174.
  • A. Wintner, A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115-117.