Bulletin of the Australian Mathematical Society

Research Article

ON A PERTURBED CONSERVATIVE SYSTEM OF SEMILINEAR WAVE EQUATIONS WITH PERIODIC-DIRICHLET BOUNDARY CONDITIONS

JINHAI CHENa1 c1 and DONAL O’REGANa2

a1 Department of Mathematical and Statistical Sciences, University of Colorado Denver, Campus Box 170, PO Box 173364, Denver, CO 80217-3364, USA (email: cjh_maths@yahoo.com.cn)

a2 Department of Mathematics, National University of Ireland, Galway, Ireland (email: donal.oregan@nuigalway.ie)

Abstract

In this paper, some existence and uniqueness results for generalized solutions to a periodic-Dirichlet problem for semilinear wave equations are given, using a global inverse function theorem. These results extend those known in the literature.

(Received June 16 2009)

2000 Mathematics subject classification

  • primary 35B10;
  • 35D05;
  • 35L05;
  • 35L20; secondary 35P05;
  • 47F05

Keywords and phrases

  • wave equation;
  • periodic-Dirichlet problem;
  • generalized solution;
  • unique existence;
  • global inverse function theorem

Correspondence:

c1 For correspondence; e-mail: cjh_maths@yahoo.com.cn