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Oscillation and nonoscillation of solutions of generalized Emden-Fowler equations. (English) Zbl 0278.34026


MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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[1] F. V. Atkinson, On second-order non-linear oscillations, Pacific J. Math. 5 (1955), 643 – 647. · Zbl 0065.32001
[2] Štefan Belohorec, On some properties of the equation \?\(^{\prime}\)\(^{\prime}\)(\?)+\?(\?)\?^{\?}(\?)=0, 0<\?<1, Mat. asopis Sloven. Akad. Vied 17 (1967), 10 – 19 (English, with Russian summary). · Zbl 0166.07702
[3] C. V. Coffman and J. S. W. Wong, On a second order nonlinear oscillation problem, Trans. Amer. Math. Soc. 147 (1970), 357 – 366. · Zbl 0223.34030
[4] C. V. Coffman and J. S. W. Wong, Second order nonlinear oscillations, Bull. Amer. Math. Soc. 75 (1969), 1379 – 1382. · Zbl 0212.43304
[5] R. H. Fowler, Further studies of Emden’s and similar differential equations, Quart. J. Math. 2 (1931), 259-288. · Zbl 0003.23502
[6] J. W. Heidel, A nonoscillation theorem for a nonlinear second order differential equation, Proc. Amer. Math. Soc. 22 (1969), 485 – 488. · Zbl 0169.42203
[7] Miloš Jasný, On the existence of an oscillating solution of the nonlinear differential equation of the second order \?\(^{\prime}\)\(^{\prime}\)+\?(\?)\?²\(^{n}\)\(^{-}\)\textonesuperior =0, \?(\?)>0, Časopis Pěst. Mat. 85 (1960), 78 – 83 (Russian, with Czech and English summaries).
[9] Jaroslav Kurzweil, A note on oscillatory solution of equation \?”+\?(\?)\?²\(^{n}\)\(^{-}\)\textonesuperior =0, Časopis Pěst. Mat. 85 (1960), 357 – 358 (Russian, with English and Czech summaries).
[10] Jack W. Macki and James S. W. Wong, Oscillation of solutions to second-order nonlinear differential equations, Pacific J. Math. 24 (1968), 111 – 117. · Zbl 0165.42402
[11] Zeev Nehari, On a class of nonlinear second-order differential equations, Trans. Amer. Math. Soc. 95 (1960), 101 – 123. · Zbl 0097.29501
[12] Zeev Nehari, Characteristic values associated with a class of non-linear second-order differential equations, Acta Math. 105 (1961), 141 – 175. · Zbl 0099.29104
[13] Zeev Nehari, A nonlinear oscillation problem, J. Differential Equations 5 (1969), 452 – 460. · Zbl 0181.09702
[14] James S. W. Wong, Some properties of solutions of \?\(^{\prime}\)\(^{\prime}\)(\?)+\?(\?)\?(\?)\?(\?\(^{\prime}\))=0. III, SIAM J. Appl. Math. 14 (1966), 209 – 214. · Zbl 0143.31803
[15] James S. W. Wong, On second order nonlinear oscillation, Funkcial. Ekvac. 11 (1968), 207 – 234 (1969). · Zbl 0184.12202
[16] C. V. Coffman and D. F. Ullrich, On the continuation of solutions of a certain non-linear differential equation, Monatsh. Math. 71 (1967), 385 – 392. · Zbl 0153.40204
[17] Charles V. Coffman, On the positive solutions of boundary-value problems for a class of nonlinear differential equations, J. Differential Equations 3 (1967), 92 – 111. · Zbl 0152.08603
[18] Stuart P. Hastings, Boundary value problems in one differential equation with a discontinuity, J. Differential Equations 1 (1965), 346 – 369. · Zbl 0142.06303
[19] Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. · Zbl 0123.21502
[20] J. W. Heidel, Uniqueness, continuation, and nonoscillation for a second order nonlinear differential equation, Pacific J. Math. 32 (1970), 715 – 721. · Zbl 0188.14301
[21] D. V. Izjumova and I. T. Kiguradze, Some remarks on the solutions of the equation \?\(^{n}\)+\?(\?)\?(\?)=0, Differencial\(^{\prime}\)nye Uravnenija 4 (1968), 589 – 605 (Russian). · Zbl 0169.10802
[22] R. M. Moroney, Note on a theorem of Nehari, Proc. Amer. Math. Soc. 13 (1962), 407 – 410. · Zbl 0115.30601
[23] Richard A. Moore and Zeev Nehari, Nonoscillation theorems for a class of nonlinear differential equations, Trans. Amer. Math. Soc. 93 (1959), 30 – 52. · Zbl 0089.06902
[24] David F. Ullrich, Boundary value problems for a class of nonlinear second-order differential equations, J. Math. Anal. Appl. 28 (1969), 188 – 210. · Zbl 0209.39402
[25] D. Willett and J. S. W. Wong, Some properties of the solutions of [\?(\?)\?\(^{\prime}\)]\(^{\prime}\)+\?(\?)\?(\?)=0, J. Math. Anal. Appl. 23 (1968), 15 – 24. · Zbl 0165.40803
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