Open Access

On positive weak solutions for a class of weighted (p(.), q(.))−Laplacian systems


Cite

[1] A. Abbassi, E. Azroul, A. Barbara, Degenerate p(x)– elliptic equation with second member in L1, ASTES journal. Vol. 2, No. 5 (2017), 45-54.Search in Google Scholar

[2] E. Acerbi & G. Mingione, Regularity results for stationary electrorheological fluids, Arch. Rational Mech. Anal. Vol. 164 (2002), 213-259.10.1007/s00205-002-0208-7Search in Google Scholar

[3] C. O. Alves & A. Moussaoui, Existence and regularity of solutions for a class of singular (p(x), q(x)) – Laplacian systems, Complex Var. Elliptic Eqts. Vol. 63, No. 2 (2017), 188-210.Search in Google Scholar

[4] A, Ambrosetti, and P. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. Vol 14 (1973), 349-381.10.1016/0022-1236(73)90051-7Search in Google Scholar

[5] F.F. Bonsall, Lectures on some fixed point theorems of functional analysis, Tata Institute of Fundamental Research, Bombay, India, 1962Search in Google Scholar

[6] H. Brézis, Analyse fonctionnelle théorie et applications, Masson, Paris, 1983.Search in Google Scholar

[7] L. Diening, Theoretical and numerical results for electrorheological fluids, PhD thesis, University of Freiberg, Germany, 2002.Search in Google Scholar

[8] D.E. Edmunds, J. Lang, A. Nekvinda, On Lp(x) norms, Proc. R. Soc. Lond. Ser. A. Vol. 455 (1999), 219-225.10.1098/rspa.1999.0309Search in Google Scholar

[9] D. Edmunds, and J. Rákosnik: Sobolev embeddings with variable exponent. Studia Math. Vol. 143 (2000), 267-293.Search in Google Scholar

[10] X.-L. Fan, “Global C1,α regularity for variable exponent elliptic equations in divergence form,” Journal of Differential Equations. Vol. 235, No.2 (2007), 397-417.Search in Google Scholar

[11] X. Fan, On the sub-supersolution method for p(x)-Laplacian equations, J. Math. Anal. Appl. Vol. 330 (2007), 665-682.10.1016/j.jmaa.2006.07.093Search in Google Scholar

[12] X.-L. Fan, Q. Zhang, and D. Zhao, “Eigenvalues of p(x)-Laplacian Dirichlet problem,” Journal of Mathematical Analysis and Applications. Vol. 302, No. 2 (2005), 306-317.Search in Google Scholar

[13] X.L. Fan and D. Zhao: On the generalized Orlicz-Sobolev space Wk,p(x)(Ω), J. Gansu Educ. College. Vol. 12, No. 1 (1998), 1-6.Search in Google Scholar

[14] D.D. Hai, R. Shivaji, An existence result on positive solutions for a class of p-Laplacian systems, Nonlinear Anal. Vol. 56 (2004), 1007-1010.10.1016/j.na.2003.10.024Search in Google Scholar

[15] S.A. Khafagy, Existence and Non-existence of Positive Weak Solutions for a Class of (p, q)-Laplacian with Different Weights, Int. J. Contemp. Math. Sciences. Vol. 6, No. 48 (2011), 2391-2400.Search in Google Scholar

[16] O. Kováčik, and J. Rákosnik: On spaces Lp(x) and Wk,p(x). Czechoslovak Math. J. Vol. 41, No. 116 (1991), 592-618.Search in Google Scholar

[17] A. Kufner, Weighted Sobolev Spaces, Teubner-Texte zur Mathematik. Teubner (1980).Search in Google Scholar

[18] O.A. Ladyzenskaja, N.N. Ural’tzeva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968.Search in Google Scholar

[19] W. Orlicz, Überkonjugierte Exponent enfolgen, Studia Math. Vol 3 (1931), 200-212.10.4064/sm-3-1-200-211Search in Google Scholar

[20] M. Ruzicka, Electrorheological fluids: Modeling and mathematical theory. Lecture Notes in Math., vol. 1748, Springer-Verlag, Berlin (2000).Search in Google Scholar

[21] M. Ruzicka: Modeling, mathematical and numerical analysis of electrorheological fluids, Appl. Math. Vol. 49, No. 6 (2004), 565-609.Search in Google Scholar

[22] J. Schauder, Der Fixpunktsalz in Funktionalraeumen, Studia Mathematica. Vol. 2 (1930), 171-180.10.4064/sm-2-1-171-180Search in Google Scholar

[23] M. Struwe, Variational Methods, Springer Verlag Berlin, Heidelberg, New York, second edition 1996.Search in Google Scholar