DOI QR코드

DOI QR Code

A MEAN CONDITION ON FORCING TERM FOR MULTIPLICITY OF PERIODIC SOLUTIONS FOR NONLINEAR DISSIPATIVE HYPERBOLIC EQUATIONS

  • KIM WAN SE (Department of Mathematics Hanyang University)
  • Published : 2005.02.01

Abstract

A condition on forcing term insuring the multiplicity of Dirichlet-periodic solutions of nonlinear dissipative hyperbolic equations is discussed. The nonlinear term is assumed to have coercive growth.

Keywords

References

  1. H. Amann, Periodic solutions for semilinear parabolic equations in 'Nonlinear Analysis: A collection of Papers in Honor of Erich Rothe' Academic Press, New York, 1978, 1-29
  2. A. Ambrosetti and G. Prodi, On the inversion of some differentiable mappings with singularities between Banach space, Ann. Mat. Pura Appl. 93 (1972), 231- 247 https://doi.org/10.1007/BF02412022
  3. H. Brezis and L. Nirenberg, Chacterization of range of some nonlinear operators and applications to boundary value problems, Ann. Scuola Norm. Sup. Pisa CI. Sci. (4) 4 (1978), 225-323
  4. S. Fucik and J. Mawhin, Generalized periodic solutions of nonlinear telegraph equations, Nonlinear Anal. Theory Methods Appl. 2 (1978), 609-617 https://doi.org/10.1016/0362-546X(78)90008-1
  5. R. E. Gains and J. L. Mawhin, Coincidence degree and nonlinear differential equations, Lecture Notes in Math. 568 (1977)
  6. N. Hirano and W. S. Kim, Existence of stable and unstable solutions for semilinear parabolic problems with a jumping nonlinearity, Nonlinear Anal. Theory Methods Appl. 26 (1996), no. 6, 1143-1160 https://doi.org/10.1016/0362-546X(94)00284-O
  7. N. Hirano and W. S. Kim, Multiplicity and stability result for semilinear parabolic equations, Discrete Contin. Dyn. Syst. Ser. B 2 (1996), no. 2, 271-280 https://doi.org/10.3934/dcds.1996.2.271
  8. N. Hirano and W. S. Kim, Periodic-Dirichlet boundary value problem semi-linear dissipative hyperbolic equations, J. Math. Anal. Appl. 148 (1990), no. 2, 371-377 https://doi.org/10.1016/0022-247X(90)90007-3
  9. W. S. Kim, A note on the existence of solution for semilinear heat equations with polynomial growth nonlonearity, Comment. Math. Univ. Carolin. 24 (1993), no. 3, 425-431
  10. W. S. Kim, Boundary value problem for nonlinear telegraph equations with superlinear growth, Nonlinear Anal. Theory Methods Appl. 12 (1988), no. 12, 1371-1376 https://doi.org/10.1016/0362-546X(88)90084-3
  11. W. S. Kim, Double-Periodic Boundary value problem for non-linear dissipative hyperbolic equations, J. Math. Anal. Appl., 145 (1990), no. 1, 1-16 https://doi.org/10.1016/0022-247X(90)90426-G
  12. W. S. Kim, Multiple Doubly-periodic solutions of semilinear dissipative hyperbolic equations, J. Math. Anal. Appl. 197 (1996), 735-748 https://doi.org/10.1006/jmaa.1996.0049
  13. W. S. Kim, Multiple existence of periodic solutions for semilinear parabolic equations with large source, Houston J. Math., to appear
  14. W. S. Kim, Multiplicity result for periodic solutions of semilinear hyperbolic equations with coercive growth nonlinearity, J. Korean Math. Soc. 38 (2001), 853-881
  15. W. S. Kim, Multiplicity result for periodic solutions of solutions of semilinear parabolic equations, Commun. Appl. Anal. 6 (2002), no. 1, 135-146
  16. W. S. Kim, Multiplicity result for semilinear dissipative hyperbolic equations, J. Math. Anal. Appl. 231 (1999), 34-46 https://doi.org/10.1006/jmaa.1998.6207
  17. W. S. Kim, Periodic-Dirichlet Boundary value problem for nonlinear dissipative hyperbolic equations at resonance, Bull. Korean Math. Soc. 26 (1989), no. 2, 221-229
  18. J. Mawhin, Periodic solutions of nonlinear telegraph equations, in Dynamical Systems, Badnarek and Cesari, eds, Academic Press, 1977, 193-210
  19. J. Mawhin and M. Willem, Multiple solutions of the periodic boundary value problem for some forced pendulum type equations, J. Differential Equations 62 (1984), no. 2, 221-229
  20. M. N. Nkashma and M. Willem, Time periodic solutions of boundary value problems for nonlinear heat, telegraph and beam equations, Seminaire de mathematique, Universite Catholique de Louvain, Rapport no. 54 (1984), vi-1-vi-32
  21. V. Stastnova and S. Fucik, Weak periodic solutions of the boundary value problem for nonlinear heat equations, Appl. Math. 24 (1979), 284-304
  22. O. Vejiovda, Partial Differential equations:time-periodic solutions, Matinus Ni- jhoft Publishers, Boston, 1982