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Keywords:
Nehari-type oscillation criteria; conjugate points; self-adjoint equation; principal solution
Summary:
Oscillation criteria of Nehari-type for the equation $(-1)^n(x^{\alpha}y^{(n)})^{(n)} + q(x)y = 0$, $\alpha\in {\bold R}$, are established. These criteria impose no sign restriction on the function $q(x)$ and generalize some recent results of the second author.
References:
[1] Coppel W.A.: Disconjugacy. Lectures Notes in Math. No. 220, Springer Verlag, Berlin-Heidelberg, 1971. MR 0460785 | Zbl 0224.34003
[2] Došlý O.: The existence of conjugate points for self-adjoint linear differential equations. Proc. Roy. Soc. Edinburgh 112A, (1989), 73-85. MR 1025455
[3] Došlý O.: Oscillation criteria for self-adjoint linear differential equations. submitted to Diff. Integral Equations.
[4] Fiedler F.: Hinreichende Oszillationkriterien für gewöhnliche Differentialoperatoren höher Ordnung. Math. Nachr. 96 (1980), 35-48. MR 0600799
[5] Fiedler F.: Oszillationkriterien vom Nehari-Typ für gewöhnliche Differentialoperatoren vierter and sechster Ordnung. Beiträge Anal. 18 (1981), 113-132. MR 0650144
[6] Fiedler F.: Oscillation criteria for a class of $2n$-order ordinary differential operators. J. Diff. Equations 42 (1981), 155-185. MR 0641646 | Zbl 0452.34031
[7] Fiedler F.: Oscillation criteria for a special class of $2n$-order ordinary differential equations. Math. Nachr. 131 (1987), 205-218. MR 0908812 | Zbl 0644.34024
[8] Glazman I.M.: Direct Methods of Qualitative Spectral Analysis of Singular Differential operators. Davey, Jerusalem, 1965. MR 0190800 | Zbl 0143.36505
[9] Lewis R.T.: Oscillation and nonoscillation criteria for some self-adjoint even order linear differential operators. Pacific J. Math. 51 (1974), 221-234. MR 0350112 | Zbl 0281.34027
[10] Müller-Pfeiffer E.: Oscillation criteria of Nehari-type for Schrödinger equation. Math. Nachr. 96 (1980), 185-194. MR 0600809
[11] Nehari Z.: Oscillation criteria for second order linear differential equations. Trans. Amer. Math. Soc. 85 (1957), 428-445. MR 0087816 | Zbl 0078.07602
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