Electron. J. Diff. Eqns., Vol. 2008(2008), No. 72, pp. 1-12.

Solvability of characteristic boundary-value problems for nonlinear equations with iterated wave operator in the principal part

Sergo Kharibegashvili, Bidzina Midodashvili

Abstract:
A characteristic boundary-value problem for a hyperbolic equation with power nonlinearity and iterated wave operator in the principal part is considered in a conical domain. Depending on the exponent of nonlinearity and spatial dimensionality of the equation, the existence and uniqueness of the solution of a boundary-value problem is established. The non-solvability of this problem is also considered here.

Submitted February 18, 2008. Published May 15, 2008.
Math Subject Classifications: 35L05, 35L35, 35L75.
Key Words: Characteristic boundary-value problem; hyperbolic equations; wave operator; power nonlinearity; nonexistence.

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Sergo Kharibegashvili
A. Razmadze Mathematical Institute
1, M. Aleksidze St., Tbilisi 0193, Georgia
email: kharibegashvili@yahoo.com
Bidzina Midodashvili
A. Razmadze Mathematical Institute
1, M. Aleksidze St., Tbilisi 0193, Georgia
email: bidmid@hotmail.com

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