Main Article Content



Nonlinear parabolic equations with deviating arguments arc studied and sufficient conditions are derived for every solution of boundary value problems to be oscillatory in a cylindrical domam. Two kinds of boundary conditions are considered. Our approach is to reduce the multi-dimensional problem to a one-dimensional problem for differential inequalities of neutral type.

Article Details

How to Cite
TANAKA, S., & YOSHIDA, N. (1997). OSCILLATIONS OF SOLUTIONS TO PARABOLIC EQUATIONS WITH DEVIATING ARGUMENTS. Tamkang Journal of Mathematics, 28(3), 169–181. https://doi.org/10.5556/j.tkjm.28.1997.4246


Ya. V. Bykov and T. Ch. Kultaev, "Oscillation of solutions of a class of parabolic equa­tions," Izv, Akad. Nauk Kirgiz. SSR No. 6 (1983), 3-9 (Russian).

L. Ya. Bykova and A. I. Marusich, "Oscillation properties of solutions of a cla.ss of parabolic equations with delay," Izv. Akad. Nauk Kirgiz. SSR. No. 2 (1989), 3-10 (Russian).

B. T. Cui, "Oscillation theorems of nonlinear parabolic equations of neutral type," Math. J. Toyama Univ. 14 (1.991), 113-123.

B. T. Cui, "Oscillation properties for parabolic equations of neutral type," Comment. Math. Univ. Carolin. 33 (1992), 581-588.

K. Gopalsamy, "Oscillations in parabolic neutral systems," Proc. Center Math. Appl. Austral. Nat. Univ. 30 (1992), 128-141.

M. K. Grammatikopoulos, G. Ladas and A. Meiniaridou, "Oscillations of second order neutral delay differential equations," Rad. Mat. 1 (1985), 267-274.

K. Kreith and G. Ladas, "Allowable delays for positive diffusion processes," Hiroshima Math. J. 15 (1985), 437-443.

T. Kusano and N. Yoshida, "Oscillation of parabolic equations with oscillating coefficients," Hiroshima Math. J. 24 (1994), 123-133.

D. P. Mishev, "Oscillation of the solutions df parabolic equations of neutral type with "maxima"," Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat. 25 (1989), 19-28.

D. P. Mishev, "Necessary and sufficient conditions for oscillation of neutral type of parabolic differential equations, " C. R. Acad. Bulgare Sci. 44 (1991), 11-14.

D. P. Mishev, "Oscillation of the solutions of non-linear parabolic equations of neutral type," Houston J. Math. 18 (1992), 259-269.

D. P. Mishcv and D. D. Bainov, "Oscillation of the solutions of parabolic differential equa­ tions of neutral type," Appl. Math. Comput. 28 (1988), 97-111.

N. Yoshida, "Oscillation of nonlinear parabolic equations with functional arguments," Hi­roshima Math. J. 16 (1986), 304-314.

N. Yoshida, "Forced oscillations of solutions of parabolic equations," Bull. Austral. Math. Soc. 36 (1987), 289-294.

J N. Yoshida, "Forced oscillations of parabolic equations with deviating arguments," Math. J. Toyama Univ. 15 (1992), 131-112.

N. Yoshida, "Forced oscillations of nonlinear parabolic equations with functional argu­ ments," Analysis 15 (1995), 71-84.

N. Yoshida, "Nonlinear oscillation of first order delay differential equations," Rocky Moun­ tain J. Math. 25 (1996), 361-373.