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    Chen, Jinhai 2015. Periodic solutions to nonlinear wave equations with spatially dependent coefficients. Zeitschrift für angewandte Mathematik und Physik, Vol. 66, Issue. 5, p. 2095.


    Chen, Jinhai 2012. Estimating Invertible Domains of Diffeomorphisms. Journal of Optimization Theory and Applications, Vol. 154, Issue. 3, p. 818.


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  • Bulletin of the Australian Mathematical Society, Volume 81, Issue 2
  • April 2010, pp. 281-288

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

  • JINHAI CHEN (a1) and DONAL O’REGAN (a2)
  • DOI: http://dx.doi.org/10.1017/S0004972709000926
  • Published online: 01 January 2010
Abstract
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.

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For correspondence; e-mail: cjh_maths@yahoo.com.cn
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]P. W. Bates , ‘Solutions of nonlinear elliptic systems with meshed spectra’, Nonlinear Anal. 4 (1980), 10231030.

[2]P. W. Bates and A. Castro , ‘Existence and uniqueness for a variational hyperbolic system without resonance’, Nonlinear Anal. 4 (1980), 11511156.

[4]A. C. Lazer , ‘Application of a lemma on bilinear forms to a problem in nonlinear oscillations’, Proc. Amer. Math. Soc. 33 (1972), 8994.

[6]J. Mawhin , ‘Conservative systems of semilinear wave equations with periodic-Dirichlet boundary conditions’, J. Differential Equations 42 (1981), 116128.

[7]J. Mawhin and J. R. Ward Jr, ‘Asymptotic nonuniform nonresonance conditions in the periodic-Dirichlet problem for semilinear wave equations’, Ann. Mat. Pura Appl. 135 (1983), 8597.

[8]R. Plastock , ‘Homeomorphisms between Banach spaces’, Trans. Amer. Math. Soc. 200 (1974), 169183.

[9]M. Radulescu and S. Radulescu , ‘Global inversion theorems and applications to differential equations’, Nonlinear Anal. 4 (1980), 951965.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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