Nonoscillation theorems for forced second order non linear differential equations
Graef, John R. ; Spikes, Paul W.
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 59 (1975), p. 694-701 / Harvested from Biblioteca Digitale Italiana di Matematica

Gli Autori provano alcuni nuovi criteri sufficienti, indipendenti da altri criteri da loro ottenuti in precedenza, perché gli integrali dell'equazione (a(t)x)+q(t)f(x)g(x)=r(t) siano tutti non oscillatori.

Publié le : 1975-12-01
@article{RLINA_1975_8_59_6_694_0,
     author = {John R. Graef and Paul W. Spikes},
     title = {Nonoscillation theorems for forced second order non linear differential equations},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {59},
     year = {1975},
     pages = {694-701},
     zbl = {0415.34033},
     mrnumber = {0486797},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1975_8_59_6_694_0}
}
Graef, John R.; Spikes, Paul W. Nonoscillation theorems for forced second order non linear differential equations. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 59 (1975) pp. 694-701. http://gdmltest.u-ga.fr/item/RLINA_1975_8_59_6_694_0/

[1] Atkinson, F. V. (1955) - On second-order non-linear oscillations, «Pacific J. Math.», 5, 643-647. | MR 72316 | Zbl 0065.32001

[2] Coffman, C. V. and Wong, J. S. W. (1972) - Oscillation and non-oscillation of solutions of generalized Emden-Fowler equations, «Trans. Amer. Math. Soc.», 167, 399-434. | MR 296413 | Zbl 0278.34026

[3] Coffman, C. V. and Wong, J. S. W. (1972) - Oscillation and non-oscillation theorems for second order ordinary differential equations, «Funkcial. Ekvac.», 15, 119-130. | MR 333337 | Zbl 0287.34024

[4] Gollwitzee, H. E. (1970) - Nonoscillation theorems for a nonlinear differential equation, «Proc. Amer. Math. Soc.», 26, 78-84. | MR 259243

[5] Graef, J. R. and Spikes, P. W. (1974) - A nonoscillation result for second order ordinary differential equations, «Rend. Accad. Sci. fis. mat. Napoli» (4), 41, 3-12. | MR 486795

[6] Graef, J. R. and Spikes, P. W. (1975) - Sufficient conditions for nonoscillation of a second order nonlinear differential equation, «Proc. Amer. Math. Soc.», 50, 289-292. | MR 369808

[7] Graef, J. R. and Spikes, P. W. (1975) - Sufficient conditions for the equation (a(t)x)+h(t,x,x)+q(t)f(x,x)=e(t,x,x) to be nonoscillatory, «Funkcial. Ekvac.», 18, 35-40. | MR 385234 | Zbl 0331.34030

[8] Hammett, M. E. (1967) - Oscillation and nonoscillation theorems for nonhomogeneous linear differential equations of second order, Ph. D. Dissertation, Auburn University. | MR 2616309

[9] Hille, E. (1948) - Nonoscillation theorems, «Trans. Amer. Math. Soc.», 64, 234-252. | MR 27925

[10] Izyumova, D. V. (1966) - On the conditions for the oscillation and nonoscillation of solutions of nonlinear second-order differential equations, «Differencial'nye Uravnenija», 2, 1572-1586. | MR 209579

[11] Izyumova, D. V. and Kiguradze, I. T. (1968) - Some remarks on solutions of the equation u′′+a(t)f(u)=0, «Differencial'nye Uravnenija», 4, 589-605. | MR 227544

[12] Kamenev, I. V. (1970) - Oscillations of solutions of nonlinear equations with multiplicatively separable right sides, «Differencial'nye Uravnenija», 6, 1510-1513. | MR 273117

[13] Keener, M. S. (1971) - On the solutions of certain linear non-homogeneous second-order differential equations, «Applicable Analysis», 1, 57-63. | MR 281997 | Zbl 0215.43802

[14] Macki, J. W. and Wong, J. S. W. (1968) - Oscillation of solutions to second order non linear differential equations, «Pacific J. Math.», 24, 111-117. | MR 224908 | Zbl 0165.42402

[15] Moore, R. A. (1955) - The behavior of solutions of a linear differential equation of second order, «Pacific J. Math.», 5, 125-145. | MR 68690 | Zbl 0064.08401

[16] Moore, R. A. and Nehari, Z. (1959) - Nonoscillation theorems for a class of nonlinear differential equations, «Trans. Amer. Math. Soc.», 93, 30-52. | MR 111897 | Zbl 0089.06902

[17] Z. Nehari (1969) - A nonlinear oscillation problem, «J. Differential Eqs.», 5, 452-460. | MR 235203 | Zbl 0181.09702