Open Access

Existence and nonexistence of positive solutions for quasilinear systems

Boundary Value Problems20062006:71534

https://doi.org/10.1155/BVP/2006/71534

Received: 14 October 2005

Accepted: 14 February 2006

Published: 6 June 2006

Abstract

The paper deals with the existence and nonexistence of positive solutions for a class of -Laplacian systems. We investigate the effect of the size of the domain on the existence of positive solution for the problem in sublinear cases. We will use fixed point theorems in a cone.

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Authors’ Affiliations

(1)
Department of Mathematical Sciences & Applied Computing, Arizona State University

References

  1. Dalmasso R: Existence and uniqueness of positive solutions of semilinear elliptic systems. Nonlinear Analysis 2000,39(5):559–568. 10.1016/S0362-546X(98)00221-1MathSciNetView ArticleMATHGoogle Scholar
  2. Deimling K: Nonlinear Functional Analysis. Springer, Berlin; 1985:xiv+450.View ArticleMATHGoogle Scholar
  3. Guo D, Lakshmikantham V: Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics in Science and Engineering. Volume 5. Academic Press, Massachusetts; 1988:viii+275.MATHGoogle Scholar
  4. Guo D, Lakshmikantham V: Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics in Science and Engineering. Volume 5. Academic Press, Massachusetts; 1988:viii+275.MATHGoogle Scholar
  5. Krasnosel'skiĭ MA: Positive Solutions of Operator Equations. Noordhoff, Groningen; 1964:381.Google Scholar
  6. O'Regan D, Wang H: Positive solutions for-laplacian systems in a ball. in preparationGoogle Scholar
  7. Wang H: On the number of positive solutions of nonlinear systems. Journal of Mathematical Analysis and Applications 2003,281(1):287–306.MathSciNetView ArticleMATHGoogle Scholar
  8. Wang H: An existence theorem for quasilinear systems. to appear in Proceedings of the Edinburgh Mathematical SocietyGoogle Scholar

Copyright

© Haiyan Wang 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.