Existence and uniqueness of solutions for a class of degenerate nonlinear elliptic equations
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 70 (2016) no. 2.

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In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations Δ(v(x) |Δu|^p-2Δu) amp;-∑_j=1^n D_j[ω_1(x) 𝒜_j(x, u, ∇u)]+ b(x,u,∇u) ω_2(x) amp; = f_0(x) - ∑_j=1^nD_jf_j(x), in Ω in the setting of the weighted Sobolev spaces.
Keywords: Degenerate nonlinear elliptic equations, weighted Sobolev spaces
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Cavalheiro, Albo Carlos. Existence and uniqueness of solutions for a class of degenerate nonlinear elliptic equations. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 70 (2016) no. 2. http://geodesic.mathdoc.fr/item/AUM_2016_70_2_a2/

[1] Cavalheiro, A. C., Existence and uniqueness of solutions for some degenerate nonlinear Dirichlet problems, J. Appl. Anal. 19 (2013), 41-54.

[2] Cavalheiro, A. C., Existence results for Dirichlet problems with degenerated p-Laplacian and p-Biharmonic operators, Appl. Math. E-Notes 13 (2013), 234-242.

[3] Chipot, M., Elliptic Equations: An Introductory Course, Birkhauser, Berlin, 2009.

[4] Drabek, P., Kufner, A., Nicolosi, F., Quasilinear Elliptic Equations with Degenerations and Singularities, Walter de Gruyter, Berlin, 1997.

[5] Fucik, S., John, O., Kufner, A., Function Spaces, Noordhoff International Publ., Leyden, 1977.

[6] Garcia-Cuerva, J., Rubio de Francia, J. L., Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, 1985.

[7] Gilbarg, D., Trudinger, N. S., Elliptic Partial Equations of Second Order, 2nd Ed., Springer, New York, 1983.

[8] Heinonen, J., Kilpelainen, T., Martio, O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford University Press, Inc., New York, 1993.

[9] Kufner, A., Weighted Sobolev Spaces, John Wiley Sons, 1985.

[10] Muckenhoupt, B., Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.

[11] Talbi, M., Tsouli, N., On the spectrum of the weighted p-Biharmonic operator with weight, Mediterr. J. Math. 4 (2007), 73-86.

[12] Torchinsky, A., Real-Variable Methods in Harmonic Analysis, Academic Press, San Diego, 1986.

[13] Turesson, B. O., Nonlinear Potential Theory and Weighted Sobolev Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 2000.

[14] Zeidler, E., Nonlinear Functional Analysis and Its Applications. Vol. I, Springer-Verlag, New York, 1990.

[15] Zeidler, E., Nonlinear Functional Analysis and Its Applications. Vol. II/B, Springer-Verlag, New York, 1990.