Nonlinear Oscillations

, 12:199 | Cite as

Applications of perturbations on accretive mappings to nonlinear elliptic systems involving (p, q)-laplacian

Article

Using perturbation results on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present some abstract results about the existence of solutions of nonlinear Neumann elliptic systems involving the (p, q)-Laplacian. The systems discussed in this paper and the method used extend and complement some previous works.

References

  1. 1.
    B. D. Calvert and C. P. Gupta, “Nonlinear elliptic boundary value problems in L p-spaces and sums of ranges of accretive operators,” Nonlin. Anal., 2, 1–26 (1978).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    C. P. Gupta and P. Hess, “Existence theorems for nonlinear noncoercive operator equations and nonlinear elliptic boundary value problems,” J. Different. Equat., 22, 305–313 (1976).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Li Wei and Zhen He, “The applications of sums of ranges of accretive operators to nonlinear equations involving the p-Laplacian operator,” Nonlin. Anal., 24, 185–193 (1995).MATHCrossRefGoogle Scholar
  4. 4.
    Li Wei, “The existence of solution of nonlinear elliptic boundary value problem,” Math. Practice Theory, 31, 360–364 (2001).MathSciNetGoogle Scholar
  5. 5.
    Li Wei and Zhen He, “The applications of theories of accretive operators to nonlinear elliptic boundary value problems in L p-spaces,” Nonlin. Anal., 46, 199–211 (2001).MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Li Wei, “The existence of a solution of nonlinear elliptic boundary value problems involving the p-Laplacian operator,” Acta Anal. Funct. Appl., 4, 46–54 (2002).MATHMathSciNetGoogle Scholar
  7. 7.
    Li Wei, “Study of the existence of the solution of nonlinear elliptic boundary value problems,” Math. Practice Theory, 34, 123–130 (2004).MathSciNetGoogle Scholar
  8. 8.
    Li Wei and Haiyun Zhou, “The existence of solutions of nonlinear boundary value problem involving the p-Laplacian operator in L s-spaces,” J. Syst. Sci. Complexity, 18, 511–521 (2005).MATHMathSciNetGoogle Scholar
  9. 9.
    Li Wei and Haiyun Zhou, “Research on the existence of solution of equation involving the p-Laplacian operator,” Appl. Math. J. Chinese Univ. Ser. B, 21, No. 2, 191–202 (2006).MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Li Wei and Haiyun Zhou, “Study of the existence of the solution of nonlinear elliptic boundary value problems,” J. Math. Res. Expos., 26, No. 2, 334–340 (2006).MATHMathSciNetGoogle Scholar
  11. 11.
    Li Wei, “The existence of solutions of nonlinear boundary value problems involving the generalized p-Laplacian operator in a family of spaces,” Acta. Anal. Func. Appl., 7, No. 4, 354–359 (2005).MATHGoogle Scholar
  12. 12.
    Li Wei and R. P. Agarwal, “Existence of solutions to nonlinear Neumann boundary value problems with generalized p-Laplacian operator,” Comput. Math. Appl., 56, No. 2, 530–541 (2008).MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    D. Pascali, Nonlinear Mappings of Monotone Type, Romania (1978).Google Scholar
  14. 14.
    T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin (1984).MATHGoogle Scholar
  15. 15.
    W. Takahashi, Nonlinear Functional Analysis—Fixed Point Theory and Its Applications, Yokohama Publ., Yokohama (2000).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHebei University of Economics and BusinessShijiazhuangChina
  2. 2.Florida Institute of TechnologyMelbourneUSA
  3. 3.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore

Personalised recommendations