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September  2003, 9(5): 1263-1275. doi: 10.3934/dcds.2003.9.1263

Generalized quasilinearization method for semilinear hyperbolic problems

T. Gnana Bhaskar 1, , S. Köksal 1, and  V. Lakshmikantham 2,

1. 

Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, United States, United States
2. 

Department of Mathematics, Florida Institute of Technology, Melbourne, FL 32901, United States

Received  November 2001 Revised  November 2002 Published  June 2003

We consider semilinear hyperbolic problem associated with a second order partial differential operator in its divergence form. We prove a comparison theorem for the weak lower and upper solutions of the problem and then apply the method of generalized quasilinearization.
Keywords: Semilinear hyperbolic problem, generalized quasilinearization method..
Mathematics Subject Classification: 34D10, 34D9.
Citation: T. Gnana Bhaskar, S. Köksal, V. Lakshmikantham. Generalized quasilinearization method for semilinear hyperbolic problems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1263-1275. doi: 10.3934/dcds.2003.9.1263
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