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On the zeros of solutions to nonlinear hyperbolic equations

Published online by Cambridge University Press:  14 November 2011

Norio Yoshida
Norio Yoshida
Affiliation:
Department of Mathematics, Faculty of Engineering, Iwate University, Morioka, Japan
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Synopsis

We consider the hyperbolic equation uxy + c(x, y, u) =f(x, y) and the wave equation

We show that, under suitable conditions, there are bounded domains in which every solution to certain problems has a zero. Characteristic initial value problems and initial boundary value problems are considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 1-2 , 1987 , pp. 121 - 129
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Cazenave, T. and Haraux, A.. Propriétés oscillatoires des solutions de certaines équations des ondes semi-lineéaires. C. R. Acad. Sci. Paris Ser. I. Math. 298 (1984), 449–452.Google Scholar
2Hsiang, W.-T. and Kwong, M. K.. On the oscillation of nonlinear hyperbolic equations. J. Math. Anal. Appl. 85 (1982), 31–45.CrossRefGoogle Scholar
3Kahane, C.. Oscillation theorems for solutions of hyperbolic equations. Proc. Amer. Math. Soc. 41 (1973), 183–188.CrossRefGoogle Scholar
4Kreith, K.. Sturmian theorems for characteristic initial value problems. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 47 (1969), 139–144.Google Scholar
5Kreith, K., Kusano, T. and Yoshida, N.. Oscillation properties of nonlinear hyperbolic equations. SIAM J. Math. Anal. 15 (1984), 570–578.CrossRefGoogle Scholar
6Kreith, K. and Pagan, G.. Qualitative theory for hyperbolic characteristic initial value problems. Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 15–24.CrossRefGoogle Scholar
7Mishev, D. P.. Oscillatory properties of the solutions of hyperbolic differential equations with “maximum”. Hiroshima Math. J. 16 (1986), 77–83.CrossRefGoogle Scholar
8Naito, M. and Yoshida, N.. Oscillation criteria for a class of higher order elliptic equations (submitted).Google Scholar
9Pagan, G.. Oscillation theorems for characteristic initial value problems for linear hyperbolic equations. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 55 (1973), 301–313.Google Scholar
10Pagan, G.. An oscillation theorem for characteristic initial value problems in linear hyperbolic equations. Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 265–271.CrossRefGoogle Scholar
11Travis, C. C.. Comparison and oscillation theorems for hyperbolic equations. Utilitas Math. 6 (1974), 139–151.Google Scholar
12Yoshida, N.. An oscillation theorem for characteristic initial value problems for nonlinear hyperbolic equations. Proc. Amer. Math. Soc. 76 (1979), 95–100.CrossRefGoogle Scholar
13Young, E. C.. Comparison and oscillation theorems for singular hyperbolic equations. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 59 (1975), 383–391.Google Scholar