Share This Article:

Multiple Solutions for a Class of Concave-Convex Quasilinear Elliptic Systems with Nonlinear Boundary Condition

Abstract Full-Text HTML XML Download Download as PDF (Size:276KB) PP. 449-455
DOI: 10.4236/am.2013.43067    4,914 Downloads   10,595 Views  
Author(s)    Leave a comment

ABSTRACT

In this paper, a quasilinear elliptic system is investigated, which involves concave-convex nonlinearities and nonlinear boundary condition. By Nehari manifold, fibering method and analytic techniques, the existence of multiple nontrivial nonnegative solutions to this equation is verified.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

L. Wang, "Multiple Solutions for a Class of Concave-Convex Quasilinear Elliptic Systems with Nonlinear Boundary Condition," Applied Mathematics, Vol. 4 No. 3, 2013, pp. 449-455. doi: 10.4236/am.2013.43067.

References

[1] J. Garcia-Azorero, I. Peral and J. D. Rossi, “A Convex-Concave Problem with a Nonlinear Boundary Condition,” Journal of Differential Equations, Vol. 198, No. 1, 2004, pp. 91-128. doi:10.1016/S0022-0396(03)00068-8.
[2] T.-F. Wu, “A Semilinear Elliptic Problem Involving Non-linear Boundary Condition and Sign-Changing Potential,” Electronic Journal of Differential Equations, Vol. 2006, No. 131, 2006, pp. 1-15.
[3] T.-F. Wu, “Multiplicity of Positive Solution of p-Laplacian Problems with Sign-Changing Weight Functions,” International Journal of Mathematical Analysis, Vol. 1, No. 9-12, 2007, pp. 557-563.
[4] T.-F. Wu, “Multiple Positive Solutions for Semilinear Elliptic Systems with Nonlinear Boundary Condition,” Applied Mathematics and Computation, Vol. 189, No. 2, 2007, pp. 1712-1722. doi:10.1080/028418501127346846.
[5] T.-S. Hsu, “Multiple Positive Solutions for a Critical Quasilinear Elliptic System with Oncave-Convex Nonlinearitiesc,” Nonlinear Analysis, Vol. 71, No. 7-8, 2009, pp. 2688-2698. doi:10.1016/ j.na.2009.01.110.
[6] T.-F. Wu, “On Semilinear Elliptic Equations Involving Concave-Convex Nonlinearities and Sign-Changing Weight Function,” Article Journal of Mathematical Analysis and Applications, Vol. 318, No. 1, 2006, pp. 253-270. doi:10.1016/j.jmaa. 2005.05.057.
[7] T.-S. Hsu and H.-L. Lin, “Multiple Positive Solutions for Singular Elliptic Equations with Concave-Convex Nonlinearities and Sign-Changing Weights,” Boundary Value Problems, Vol. 2009, 2009, Article ID: 584203.
[8] L. Wang, Q. Wei and D. Kang, “Existence and Multiplicity of Positive Solutions to Elliptic Systems Involving Critical Exponents,” Journal of Mathematical Analysis and Applications, Vol. 383, No. 2, 2011, pp. 541-552. doi:10.1016/j.jmaa. 2011.05.053.
[9] K. Brown and Y. Zhang, “The Nehari Manifold for a Semilinear Elliptic Equation with a Sign-Changing Weight Function,” Journal of Differential Equations, Vol. 193, No. 2, 2003, pp. 481-499. doi:10.1016/S0022-0396(03)00121-9.
[10] G. Tarantello, “On Nonhomogeneous Elliptic Equations Involving Critical Sobolev Exponent,” Annales De L Institut Henri Poincare-Analyse Non Lineaire, Vol. 9, No. 3, 1992, pp. 281-304.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.