Abstract
We establish sufficient conditions for oscillation and nonoscillation of regular solutions of the secondorder differential equation Sign y=0, where λ<1 and p: [a,ω[→ ℝ, −∞< a < ω≤+∞ is a locally summable function.
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References
A. Elbert, “A half-linear second order differential equation,”Coll. Math. J. Bolyai,30, 153–180 (1979).
A. Elbert, “The Wronskian and the half-linear differential equation,”Stud. Sci. Math. Hung., 101–105 (1980).
E. Hille, “Non-oscillation theorems,”Trans. Am. Math. Soc.,64, 234–252 (1948).
M. Rab, “Kriterien für die oscillation Lösungen Differentialglechung (p(x)y′)′+q (x) y=0,”Casopis pro Pest. Mat.,84, 335–370 (1959).
J. S. W. Wong, “Oscillation and nonoscillation of solutions of second order linear differential equations with integrable coefficients,”Trans. Am. Math. Soc.,144, 197–215 (1969).
D. Willett, “Classification of second order linear differential equations with respect to oscillations,”Adv. Math.,3, 594–623 (1969).
D. D. Mirzov, “On oscillation of solutions of a system of differential equations,”Mat. Zametki,23, No. 3, 401–404 (1978).
J. D. Mirzov, “On some analogs of Sturm's and Kneser's theorems for nonlinear systems,”J. Math. Anal. Appl.,53, No. 1, 418–425 (1976).
A. Kneser, “Untersuchungen über die reelen Nullstellen der Integral linearer Differentialgleichungen,”Math. Ann.,42, 409–435 (1893).
M. Bocher, “On regular singular points of linear differential equations of the second order whose coefficients are not necessarily analytic,”Trans. Am. Soc.,1, 40–53 (1900).
I. T. Kiguradze, “On oscillation of solutions of the equationu(m+at)|u|n, signu=0,”Mat. Sb.,65 (107), No. 2, 172–187 (1966).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 833–841, July, 1994.
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Evtukhov, V.M. On conditions for oscillation and nonoscillation of the solutions of a semilinear second-order differential equation. Ukr Math J 46, 912–921 (1994). https://doi.org/10.1007/BF01056668
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DOI: https://doi.org/10.1007/BF01056668