×

Forced oscillation of certain neutral hyperbolic equations with continuous distributed deviating arguments. (English) Zbl 1165.35474

Summary: We consider certain hyperbolic equations with continuous distributed deviating arguments, and sufficient conditions are presented for every solution of some boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce multi-dimensional problems to one-dimensional problems by using some integral means of solutions.

MSC:

35R10 Partial functional-differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Courant, R.; Hilbert, D., Methods of Mathematical Physics, vol. I (1966), Interscience: Interscience New York · Zbl 0729.00007
[2] Deng, L. H., Oscillation criteria for certain hyperbolic functional differential equations with Robin boundary condition, Indian J. Pure Appl. Math., 33, 1137-1146 (2002) · Zbl 1010.35110
[3] Deng, L. H.; Ge, W. G., Oscillation for certain delay hyperbolic equations satisfying the Robin boundary condition, Indian J. Pure Appl. Math., 32, 1269-1274 (2001) · Zbl 1027.35145
[4] Deng, L. H.; Ge, W. G.; Wang, P. G., Oscillation of hyperbolic equations with continuous deviating argument under the Robin boundary condition, Soochow J. Math., 29, 1-6 (2003) · Zbl 1033.35129
[5] Kreith, K.; Kusano, T.; Yoshida, N., Oscillation properties of nonlinear hyperbolic equations, SIAM J. Math. Anal., 15, 570-578 (1984) · Zbl 0545.35062
[6] Kusano, T.; Naito, M., Nonlinear oscillation of second order differential equations with retarded arguments, Ann. Mat. Pura Appl., 4, 106, 171-185 (1975) · Zbl 0316.34083
[7] Liu, X. Z.; Fu, X. L., Oscillation criteria for nonlinear inhomogeneous hypobolic equations with distributed deviating arguments, J. Appl. Math. Stoch. Anal., 9, 21-31 (1996)
[8] Mishev, D. P.; Bainov, D. D., Oscillation properties of the solutions of hyperbolic equations of neutral type, (Differential Equations: Qualitative Theory (Szeged, 1984). Differential Equations: Qualitative Theory (Szeged, 1984), Colloq. Math. Soc. Janos Bolyai 47, vol. II (1987), North-Holland: North-Holland Amsterdam), 771-780 · Zbl 0651.35052
[9] Tanaka, S., Oscillation criteria for a class of second order forced neutral differential equations, Math. J. Toyama Univ., 27, 71-90 (2004) · Zbl 1079.34053
[10] Tanaka, S.; Yoshida, N., Forced oscillation of certain hyperbolic equations with continuous distributed deviating arguments, Ann. Polon. Math., 85, 37-54 (2005) · Zbl 1083.35128
[11] Tao, Y.; Yoshida, N., Oscillation of nonlinear hyperbolic equations with distributed deviating arguments, Toyama Math. J., 28, 27-40 (2005) · Zbl 1107.35405
[12] Wang, P. G., Forced oscillation of a class of delay hyperbolic equation boundary value problem, Appl. Math. Comput., 103, 15-25 (1990)
[13] Wang, P. G., Oscillation of certain neutral hyperbolic equations, Indian J. Pure Appl. Math., 31, 949-956 (2000) · Zbl 0961.35170
[14] Wang, P. G.; Yu, Y. H., Oscillation criteria for a nonlinear hyperbolic boundary value problem, Appl. Math. Lett., 12, 91-98 (1999) · Zbl 0941.35043
[15] Yoshida, N., An oscillation theorem for characteristic initial value problems for nonlinear hyperbolic equations, Proc. Amer. Math. Soc., 76, 95-100 (1979) · Zbl 0421.35003
[16] Yoshida, N., Oscillation of nonlinear parabolic equations with functional arguments, Hiroshima Math. J., 16, 305-314 (1986) · Zbl 0614.35048
[17] Yoshida, N., Oscillation criteria for a class of hyperbolic equations with functional arguments, Kyungpook Math. J., 41, 75-85 (2001) · Zbl 0988.35162
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.