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Oscillation criteria for solution to partial dynamic equations on time scales. (English) Zbl 1488.35330

Summary: We consider the oscillatory behavior of solutions to partial dynamic equation on time scales. We establish several oscillation criteria by applying a Riccati transformation. Examples are provided to justify our results.

MSC:

35L10 Second-order hyperbolic equations
26E70 Real analysis on time scales or measure chains
34N05 Dynamic equations on time scales or measure chains
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[1] [1] R.P. Agarwal, M. Bohner and S.H. Saker, Oscillation of second order delay dynamic equations, Can. Appl. Math. Q. 13, 1-18, 2005. · Zbl 1126.39003
[2] [2] C.D. Ahlbrandt and C. Morian, Partial differential equations on time scales, J. Com- put. Appl. Math. 141, 35-55, 2002. · Zbl 1134.35314
[3] [3] M. Bohner and G.S. Guseinov, Partial differentiation on time scales, Dynam. Systems Appl. 13, 351-379, 2004. · Zbl 1090.26004
[4] [4] M. Bohner and A. Peterson, Dynamic Equations on Time Scale, An Introduction with Applications, Birkhäuser, Boston, 2001. · Zbl 0978.39001
[5] [5] M. Bohner and S.H. Saker, Oscillation of second order nonlinear dynamic equations on time scales, Rocky Mountain J. Math. 34, 1239-1254, 2004. · Zbl 1075.34028
[6] [6] M. Bohner, L. Erbe and A. Peterson, Oscillation for nonlinear second order dynamic equations on time scales, J. Math. Anal. Appl. 301, 491-507, 2005. · Zbl 1061.34018
[7] [7] L. Erbe, A. Peterson and S.H. Saker, Oscillation criteria for second order nonlinear dynamic equations on time scales, J. Lond. Math. Soc. 67 (3), 701-714, 2003. · Zbl 1050.34042
[8] [8] L.C. Evans, Partail Differential Equations, American Math. Society, Graduate Studies in Mathematics Vol. 19, second ed., 2010. · Zbl 1194.35001
[9] [9] P. Hasil and M. Veselý, Oscillation and nonoscillation criteria for linear and half linear difference equations, J. Math. Anal. Appl. 452 (1), 401-428, 2017. · Zbl 1372.39015
[10] [10] J. Hoffacker, Basic partial dynamic equations on time scales, J. Difference Equ. Appl. 8 (4), 307-319, 2002. · Zbl 1003.39018
[11] [11] B. Jackson, Partial dynamic equations on time scales, J. Comput. Appl. Math. 186 (2), 391-415, 2006. · Zbl 1081.39013
[12] [12] P. Prakash and S. Harikrishnan, Oscillation of solutions of impulsive vector hyperbolic differential equations with delays, Appl. Anal. 91 (3), 459-473, 2012. · Zbl 1242.35218
[13] [13] P. Prakash, S. Harikrishnan and M. Benchohra, Oscillation of certain nonlinear frac- tional partial differential equation with damping term, Appl. Math. Lett. 43, 72-79, 2015. · Zbl 1406.35475
[14] [14] S.H. Saker, Oscillation criteria of second order half linear dynamic equations on time scales, J. Comput. Appl. Math. 177 (2), 375-387, 2005. · Zbl 1082.34032
[15] [15] Y. Shoukaku and N. Yoshida, Osillations of nonlinear hyperbolic equations with func- tional arguments via Riccati method, Appl. Math. Comput. 217, 143-151, 2010. · Zbl 1203.35017
[16] [16] S. Sun, Z. Han and C. Zhang, Oscillation of second order delay dynamic equations on time scales, J. Appl. Math. Comput. 30 (1-2), 459-468, 2009. · Zbl 1180.34069
[17] [17] Q. Zhang, Oscillation of second order half linear delay dynamic equations with damp- ing on time scales, J. Comput. Appl. Math. 235 (5), 1180-1188, 2011. · Zbl 1207.34087
[18] [18] Q. Zhang and L. Gao, Oscillation of second order nonlinear delay dynamic equations with damping on time scales, J. Appl. Math. Comput. 37 (1-2), 145-158, 2011. · Zbl 1368.34101
[19] [19] X. Zhou, C. Liu and W.-S.Wang, Interval oscillation criteria for nonlinear differential equations with impulses and variable delay, Appl. Math. Lett. 85, 150-156, 2018. · Zbl 1403.34051
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