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 AM  Vol.4 No.3 , March 2013
Multiple Solutions for a Class of Concave-Convex Quasilinear Elliptic Systems with Nonlinear Boundary Condition
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.
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.

 
 
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