Positive coefficients case and oscillation

Ján Ohriska

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1998)

  • Volume: 18, Issue: 1-2, page 5-17
  • ISSN: 1509-9407

Abstract

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We consider the second order self-adjoint differential equation (1) (r(t)y’(t))’ + p(t)y(t) = 0 on an interval I, where r, p are continuous functions and r is positive on I. The aim of this paper is to show one possibility to write equation (1) in the same form but with positive coefficients, say r₁, p₁ and to derive a sufficient condition for equation (1) to be oscillatory in the case p is nonnegative and ∫ ∞ [ 1 / r ( t ) ] d t converges.

How to cite

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Ján Ohriska. "Positive coefficients case and oscillation." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 18.1-2 (1998): 5-17. <http://eudml.org/doc/275896>.

@article{JánOhriska1998,
abstract = {We consider the second order self-adjoint differential equation (1) (r(t)y’(t))’ + p(t)y(t) = 0 on an interval I, where r, p are continuous functions and r is positive on I. The aim of this paper is to show one possibility to write equation (1) in the same form but with positive coefficients, say r₁, p₁ and to derive a sufficient condition for equation (1) to be oscillatory in the case p is nonnegative and $∫^∞ [1/r(t)]dt$ converges.},
author = {Ján Ohriska},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {oscillation theory; positive coefficients; selfadjoint equation},
language = {eng},
number = {1-2},
pages = {5-17},
title = {Positive coefficients case and oscillation},
url = {http://eudml.org/doc/275896},
volume = {18},
year = {1998},
}

TY - JOUR
AU - Ján Ohriska
TI - Positive coefficients case and oscillation
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1998
VL - 18
IS - 1-2
SP - 5
EP - 17
AB - We consider the second order self-adjoint differential equation (1) (r(t)y’(t))’ + p(t)y(t) = 0 on an interval I, where r, p are continuous functions and r is positive on I. The aim of this paper is to show one possibility to write equation (1) in the same form but with positive coefficients, say r₁, p₁ and to derive a sufficient condition for equation (1) to be oscillatory in the case p is nonnegative and $∫^∞ [1/r(t)]dt$ converges.
LA - eng
KW - oscillation theory; positive coefficients; selfadjoint equation
UR - http://eudml.org/doc/275896
ER -

References

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  1. [1] J.H. Barrett, Oscillation theory of ordinary linear differential equations, Advances in Math. 3 (1969), 415-509. Zbl0213.10801
  2. [2] M. Cecchi, M. Marini and G. Villari, Integral criteria for a classification of solutions of linear differential equations, J. Differential Equations 99 (1992), 381-397. Zbl0761.34009
  3. [3] B.J. Harris On the oscillation of solutions of linear differential equations, Mathematika 31 (1984), 214-226. 
  4. [4] Ch. Huang, Oscillation and nonoscillation for second order linear differential equations, J. Math. Anal. Appl. 210 (1997), 712-723. Zbl0880.34034
  5. [5] W. Leighton, Principal quadratic functionals and self-adjoint second-order differential equations, Proc. Nat. Acad. Sci. 35 (1949), 192-193. Zbl0032.34603
  6. [6] J. Ohriska, Oscillation of second order delay and ordinary differential equation, Czechoslovak Math. J. 34 (109) (1984), 107-112. Zbl0543.34054
  7. [7] J. Ohriska, Oscillation of differential equations and v-derivatives, Czechoslovak Math. J. 39 (114) (1989), 24-44. Zbl0673.34044
  8. [8] J. Ohriska, On the oscillation of a linear differential equation of second order, Czechoslovak Math. J. 39 (114) (1989), 16-23. Zbl0673.34043
  9. [9] R. Oláh, Integral conditions of oscillation of a linear differential equation, Math. Slovaca 39 (1989), 323-329. Zbl0685.34029
  10. [10] W.T. Reid, Sturmian theory for ordinary differential equations, Springer-Verlag New York Inc. (1980). Zbl0459.34001
  11. [11] D. Willett, Classification of second order linear differential equations with respect to oscillation, Advances in Math. 3 (1969), 594-623. Zbl0188.40101

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