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  • 1 Faculty of Science, Institute of Mathematics and Informatics, 1000 Skoplje, Macedonia
  • | 2 Faculty of Engineering, Kosovska Mitrovica, Serbia
  • | 3 Faculty of Mechanical Engineering, Dositejeva 19, 36000 Kraljevo, Serbia
  • | 4 School for Pedagogues Gnjilane, Bujanovac, Serbia
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Abstract

It is shown that Sturm theorems, formulated in the 1830’s ([1], [2], [3] and [4]) and valid for second order linear homogeneous differential equation L(y)≡y″+a(x)y′+b(x)y=0, could as well be formulated for the class of nonhomogeneous linear differential equations L(y)=f(x). Criteria for the existence of oscillatory solutions of nonhomogeneous equations, as well as more exact locations of the zeros are given.

  • [1] Sturm, C. 1836 Sur les équations linéaires du second order J. Math. Pures Appl. 1 106186.

  • [2] Ince, E. L. 1939 Ordinary Differential Equations ONTI Kharkov in Russian.

  • [3] Coddington, E. A., Levinson, N. 1955 Theory of Ordinary Differential Equations IL Moscow in Russian.

  • [4] Sansone, G. 1952 Ordinary Differential Equations IL Moscow in Russian.

  • [5] Suyama, Y. 1954 On the zeros of solutions of second order linear differential equation Mem. Fac. Sci. Kyusyu Univ. Ser. A 8 201205 .

  • [6] Kneser, A. 1893 Untersuchungen über die reelen Nullstellen der Integrale lineare Differentialgleichungen Math. Ann. 42 409435 .

  • [7] Biernacki, M. 1953 Sur le nombre minimum des zéros des intègrales de l’équation y(n)+A(x)y=0 Univ. Mariae Curie-Sklodowska 7 1518.

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  • [8] Dimitrovski, D., Rajović, M., Stoiljković, R. 2007 On types, form and supremum of the solutions of the linear differential equation of the second order with entire coefficients Applicable Analysis and Discrete Mathematics 1 360370 .

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  • [9] Dimitrovski, D., Cvejić, S., Rajović, M., Lekić, M., Rajović, V. and Dimitrovski, A., 200 Years of Qualitative Analysis of Differential Equations, Monograph, University of Kosovska Mitrovica, Faculty of Science (2008) (in Serbian).

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  • [10] Tiryaki, A., Yaman, S. 2001 Oscilatory behavior of a class of nonlinear differential equations of third order Acta Math. Sci. 21 B 182188.

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  • [11] Aktas, M. F., Tiryaki, A., Zafer, A. 2010 Oscilation criteria for third order nonlinear functional differential equations Appl. Math. Lett. 10.1016/j.aml.2010.03.003.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
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Address
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Springer Nature Switzerland AG
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)