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On the zeros of solutions of nonhomogeneous third order differential equations. (English) Zbl 0758.34022

The comparison of the oscillatory and nonoscillatory behaviour of the solutions to the differential equation \((r(t)y'')'+q(t)y'+p(t)y=f(t)\) and its associated homogeneous equation as well as some related problems are studied. Here \(p,q,r,f\in C([0,\infty),\mathbb{R})\) and \(r(t)>0\).

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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References:

[1] L. Erbe: Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equations. Pacific J. Math. 64 (1976), 369-385. · Zbl 0339.34030
[2] M. Gera: Some oscillation conditions for a linear third order differential equations. Soviet Math. Dokl. 36 (2) (1988), 277-280. · Zbl 0655.34024
[3] M. Greguš: Third Order Linear Differential Equations. D. Reidel Pub. Co. Boston, Tokyo, 1987. · Zbl 0602.34005
[4] M. Hanan: Oscillation criteria for third order linear differential equations. Pacific J. Math. 11 (1961), 919-944. MR 26 # 2695. · Zbl 0104.30901
[5] G. Jayaraman N. Padmanabhan, R. Mehrotra: Entry flow into a circular tube of slowly varying cross-section. Fluid Dynamics Research 1 (1986), 131-144. The Japan Society of Fluid Mechanics.
[6] Gary D. Jones: Oscillation criteria for third order differential equations. SIAM J. Math. Anal. 7 (1976), 13-15. · Zbl 0342.34019
[7] Gary D. Jones: Oscillation properties of \(y" + p(x) y = f(x)\). Academia Nazionale Del Lincei. 57 (1974), 337-341. · Zbl 0349.34023
[8] M. S. Keener: On the solutions of certain linear nonhomogeneous second-order differential equations. Applicable Analysis 1 (1971), 57-63. · Zbl 0215.43802
[9] A. C. Lazer: The behaviour of solutions of the differential equation \(y'" + p(x) y' + q(x) y = = 0\). Pacific J. Math. 17 (1966), 435-466. MR 33 # 1552. · Zbl 0143.31501
[10] Zeev Nehari: Oscillation criteria for second-order linear differential equations. Trans. Amer. Math. Soc. 85 (1957), 428-444. · Zbl 0078.07602
[11] W. Leighton, Z. Nehari: On the oscillation of solutions of self-adjoint linear differential equations of the fourth order. Trans. Amer. Math. Soc. 89 (1958), 325-377. · Zbl 0084.08104
[12] N. Parhi, P. Das: On nonoscillation of third order differential equations. Communicated. · Zbl 0815.34022
[13] R. E. Sitter, S. C. Tefteller: Oscillation of a fourth order nonhomogeneous differential equation. J. Math. Anal. Appl. 59 (1977), 93-104. · Zbl 0358.34029
[14] A. Skidmore, W. Leighton: On the differential equation \(u" + p(x)y = f(x)\). J. Math. Anal. Appl. 43 (1973), 46-55. · Zbl 0287.34031
[15] C. A. Swanson: Comparison and Oscillation Theory of Linear Differential Equations. Academic Press, New York and London, 1968. · Zbl 0191.09904
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