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XU, ZHITING. OSCILLATION CRITERIA FOR CERTAIN DAMPED PDE'S WITH p-LAPLACIAN. Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 129-142. doi: 10.1017/S0017089507004004
@article{10_1017_S0017089507004004,
author = {XU, ZHITING},
title = {OSCILLATION {CRITERIA} {FOR} {CERTAIN} {DAMPED} {PDE'S} {WITH} {p-LAPLACIAN}},
journal = {Glasgow mathematical journal},
pages = {129--142},
year = {2008},
volume = {50},
number = {1},
doi = {10.1017/S0017089507004004},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507004004/}
}
TY - JOUR AU - XU, ZHITING TI - OSCILLATION CRITERIA FOR CERTAIN DAMPED PDE'S WITH p-LAPLACIAN JO - Glasgow mathematical journal PY - 2008 SP - 129 EP - 142 VL - 50 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507004004/ DO - 10.1017/S0017089507004004 ID - 10_1017_S0017089507004004 ER -
[1] 1.Agarwal, R. P., Grace, S. R. and O'Regan, D., Oscillation theory for difference and functional differential equations (Kluwer, 2000). Google Scholar | DOI
[2] 2.Agarwal, R. P., Grace, S. R. and O'Regan, D., Oscillation theory for second order linear, half-linear, superlinaer and sublinear dynamic equations (Kluwer, 2002). Google Scholar | DOI
[3] 3.Díaz, J. I., Nonlinear partial differential equations and free boundaries, Vol. I. Elliptic equations, Pitman, London, 1985. Google Scholar
[4] 4.Došlý, O. and Mařík, R., Nonexistence of positive solutions of PDE's with p-Laplacian, Acta. Math. Hungar. 90 (2001), 89–107. Google Scholar | DOI
[5] 5.Fite, W. B., Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc. 19 (1918), 341–352. Google Scholar | DOI
[6] 6.Hardy, G., Littlewood, J. E. and Pólya, G., Inequalties, Second edition (Cambridge University Press, 1999). Google Scholar
[7] 7.Hartman, P., Ordinary differential equations (Wiley, 1964). Google Scholar
[8] 8.Kusano, T., Jaroš, J. and Yoshida, N., A Picone-type identity and Sturmian comparison and oscillation theorems for a class of half-linear partial differential equations of second order, Nonlinear Anal. 40 (2007), 381–395. Google Scholar | DOI
[9] 9.Ladde, G. S., Lakshmikantham, V. and Zhang, B. G., Oscillation theory of differential equations with deviating argument (Marcel Dekker, 1987). Google Scholar
[10] 10.Kamenev, I. V., Oscillation of solutions of a second order differential equation with an “integrally small’ coefficient, Differencial'nye Uravnenija. 13 (1977), 2141–2148 (in Russian). Google Scholar
[11] 11.Mařík, R., Oscillation criteria for PDE with p-Laplacian via the Riccati technique, J. Math. Anal. Appl. 248 (2000), 290–308. Google Scholar | DOI
[12] 12.Mařík, R., Hartman-Wintner type theorem for PDE with p-Laplacian, Proc. Colloq. Qual. Theory Differ. Equ. 18 (2000), 1–7. Google Scholar
[13] 13.Mařík, R., Riccati-type inequality and oscillation criteria for a half-linear PDE with damping, Electron J. Diff. Eqs. 11 (2004), 1–17. Google Scholar
[14] 14.Mařík, R., Integral averages and oscillation criteria for a half-linear partial differential equation, Appl. Math. Comput. 150 (2004), 69–87. Google Scholar
[15] 15.Mařík, R., Interval-type oscillation criteria for half-linear PDE with damping, Appl. Appl. Math. 1 (2006), 1–10. Google Scholar
[16] 16.Noussair, E. S. and Swanson, C. A., Oscillation of semilinear elliptic inequalities by Riccati transformation, Canad. J. Math. 32 (4) (1980) 908–923. Google Scholar | DOI
[17] 17.Swanson, C. A., Comparison and oscillatory theory of linear differential equations (Academic Press, 1968). Google Scholar
[18] 18.Swanson, C. A., Semilinear second order elliptic oscillation, Canad. Math. Bull. 22 (1979), 139–157. Google Scholar | DOI
[19] 19.Usami, H., Some oscillation theorems for a class of quasilinear elliptic equations, Ann. Math. Pura. Appl. 175 (1998) 277–283. Google Scholar | DOI
[20] 20.Wintner, A., A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115–117. Google Scholar | DOI
[21] 21.Xu, Z., Oscillation of second order elliptic partial differential equations with a “weakly integrally small” coefficient, J. Sys & Math. Scis. 18 (1998), 478–484. (in Chinese). Google Scholar
[22] 22.Xu, Z., Oscillation properties for quasilinear elliptic equations in divergence form, J. Sys & Math. Scis. 24 (2004), 85–95 (in Chinese). Google Scholar
[23] 23.Xu, Z., Riccati inequality and oscillation criteria for PDE with p-Laplacian, J. Inequal Appl. 2006, Art. ID 63061, 1–10. Google Scholar
[24] 24.Xu, Z. and Xing, H., Oscillation criteria of Kamenev-type for PDE with p-Laplacian, Appl. Math. Comput. 145 (2003), 735–745. Google Scholar
[25] 25.Xu, Z. and Xing, H., Oscillation criteria for PDE with p-Laplacian involving general means, Ann. Mat. Pura Appl. 184 (2005), 395–406. Google Scholar | DOI
[26] 26.Zhang, B. G., Zhao, T. and Lalli, B. S., Oscillation criteria for nonlinear second order elliptic differential equations, Chin. Ann. Math. Ser. B. 17 (1996), 89–102. Google Scholar
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