Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

Subject Areas : History and biography

F. M. Yaghoobi ¹ , J. Shamshiri ²

1 - Department of Mathemetics, College of Science, Hamedan Branch, Islamic Azad University, Hamedan, Iran
2 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Received: 2015-12-29 Accepted : 2016-03-01 Published : 2016-06-01

Keywords:

References:

[1] A. Aghajani and J. Shamshiri and F. M. Yaghoobi, Existence and multiplicity of positive solutions for a class of nonlinear elliptic problems, Turk. J. Math (2012) doi:10.3906/mat-1107-23.

[2] A. Aghajani and J. Shamshiri, Multilicity of positive solutions for quasilinear elliptic p-Laplacian systems, E. J. D. E. 111 (2012) 1-16.

[3] A. Aghajani and F.M. Yaghoobi and J. Shamshiri, Multiplicity of positive solutions for a class of quasilinear elliptic p-Laplacian problems with nonlinear boundary conditions, Journal of Information and computing Science 8 (2013) 173-182.

[4] Y. Bozhkov and E. Mitidieri, Existence of multiple solutions for quasilinear systems via fibering method, Journal of Differential Equations 190 (2003) 239-267.

[5] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2010.

[6] K. J. Brown and T.-F.Wu, A semilinear elliptic system involving nonlinear boundary condition and signchanging weight function, J. Math.Anal. Appl. 337 (2008) 1326-1336.

[7] K. J. Brown and Y. Zhang, The Nehari manifold for a semilinear elliptic problem with a sign changing weight function, J. Differential Equations 193 (2003) 481-499.

[8] C. M. Chu and C. L. Tang, Existence and multiplicity of positive solutions for semilinear elliptic systems with Sobolev critical exponents, Nonlinear Anal 71 (2009) 5118-5130.

[9] P. Drabek and S. I. Pohozaev, Positive solutions for the p-Laplacian: application of the fibering method, Proc. Royal Soc. Edinburgh Sect. A 127 (1997) 703-726.

[10] I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974) 324-353.

[11] H. Fan, Multiple positive solutions for a critical elliptic system with concave and convex nonlinearities, Nonlinear Anal. Real World Appl. 18 (2014) 1422.

[12] M. F. Furtado a and J. P. P. da Silva, Multiplicity of solutions for homogeneous elliptic systems with critical growth, J.Math. Anal. Appl. 385 (2012) 770-785.

[13] T. -s. Hsu, Multiple positive solutions for a quasilinear elliptic system involving concave-convex nonlinearities and sign changing weight functions, Internat. J. Math. Math. Sci. (2012) doi:10.1155 (2012) 109-214.

[14] Feng-Yun Lu, The Nehari manifold and application to a semilinear elliptic system, Nonlinear Analysis 71 (2009) 3425-3433

[15] Y. Shen and J. Zhang, Multiplicity of positive solutions for a semilinear p-Laplacian system with Sobolev critical exponent, Nonlinear Analysis 74 (2011) 1019-1030.

[16] M. Struwe, Variational methods, Springer, Berlin, 1990.

[17] T. F. Wu, The Nehari manifold for a semilinear elliptic system involving sign-changing weight functions, Nonlin. Analysis 68 (6) (2008), 1733-1745.