Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 72, pp. 1-12.

Title: Solvability of characteristic boundary-value problems for
       nonlinear equations with iterated wave operator in the
       principal part
  
Authors: Sergo Kharibegashvili (A. Razmadze Math. Institute, Georgia)
         Bidzina Midodashvili  (A. Razmadze Math. Institute, Georgia)

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.