Generalized quasilinearization method for semilinear hyperbolic problems

T. Gnana Bhaskar; S. Köksal; V. Lakshmikantham

doi:10.3934/dcds.2003.9.1263

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2003, Volume 9, Issue 5: 1263-1275. Doi: 10.3934/dcds.2003.9.1263

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Generalized quasilinearization method for semilinear hyperbolic problems

1.
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901
2.
Department of Mathematics, Florida Institute of Technology, Melbourne, FL 32901

Received: October 31, 2001

Revised: October 31, 2002

Published: August 2003

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Abstract

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, 34D99.

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