Acta Mathematica Sinica

, Volume 11, Issue 4, pp 439–445 | Cite as

Existence of periodic solutions of nonlinear systems with nonlinear boundary conditions

  • Xiang Xiaolin 
  • Luo Tao 
Article

Abstract

In this paper we consider the periodic solutions of nonlinear parabolic systems with nonlinear boundary conditions. By constructing the Poincare operator, we obtain the existence of\(W_p^{2\beta }\)-periodic weak solutions under some reasonable assumptions.

Keywords

Nonlinear parabolic systems Nonlinear boundary conditions Periodic solutions Semigroup 

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References

  1. [1]
    Amann, H.,Parabolic evolution equations and nonlinear boundary conditions, J. Diff. Eqs.72(1988), 201–269.CrossRefGoogle Scholar
  2. [2]
    Ruan Weihua,Bounded solutions for reaction-diffusion systems with nonlinear boundary conditions, Nonlinear Anal. T.M.A.,14:2(1990), 1051–1077.CrossRefGoogle Scholar
  3. [3]
    Pao, C. V.,On nonlinear reaction-diffuaion system, J. Math. Anal. Appl.,87(1882), 165–198.CrossRefGoogle Scholar
  4. [4]
    Bergh, J. & Leofstroem, J., Interpolation Spaces: An Introduction, Springer-Verlag, Berlin, New York, 1975.Google Scholar
  5. [5]
    Gilbarg, D. & Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Springer-verlag, Berlin, Heidelberg, New York, 1977.Google Scholar
  6. [6]
    Walter, W., Differential and Inequalities, Ergebniss der Mathematik Und ihrer Grenzgebiete Band 55, Springer-Verlag, New York, Heidelberg, Berlin, 1970.Google Scholar
  7. [7]
    Aronson, D., Grandall G. and Peletier, L. A.,Stabilization of solutions of a degenerate nonlinear problem, Nonlinear Anal.,6(1982), 1001–1022.CrossRefGoogle Scholar

Copyright information

© Science Press 1995

Authors and Affiliations

  • Xiang Xiaolin 
    • 1
  • Luo Tao 
    • 2
  1. 1.Department of MathematicsGuizhou UniversityGuiyangChina
  2. 2.Institute of MathematicsAcademia SinicaBeijingChina

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