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2016 | 70 | 2 |
Tytuł artykułu

Existence and uniqueness of solutions for a class of degenerate nonlinear elliptic equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations \begin{align} {\Delta}(v(x)\, {\vert{\Delta}u\vert}^{p-2}{\Delta}u) &-\sum_{j=1}^n D_j{\bigl[}{\omega}_1(x) \mathcal{A}_j(x, u, {\nabla}u){\bigr]}+ b(x,u,{\nabla}u)\, {\omega}_2(x)\\ & = f_0(x) - \sum_{j=1}^nD_jf_j(x), \ \ {\rm in } \ \ {\Omega} \end{align} in the setting of the weighted Sobolev spaces.
Rocznik
Tom
70
Numer
2
Opis fizyczny
Daty
wydano
2016
online
2016-12-24
Twórcy
Bibliografia
  • Cavalheiro, A. C., Existence and uniqueness of solutions for some degenerate nonlinear Dirichlet problems, J. Appl. Anal. 19 (2013), 41-54.
  • Cavalheiro, A. C., Existence results for Dirichlet problems with degenerated p-Laplacian and p-Biharmonic operators, Appl. Math. E-Notes 13 (2013), 234-242.
  • Chipot, M., Elliptic Equations: An Introductory Course, Birkhauser, Berlin, 2009.
  • Drabek, P., Kufner, A., Nicolosi, F., Quasilinear Elliptic Equations with Degenerations and Singularities, Walter de Gruyter, Berlin, 1997.
  • Fucik, S., John, O., Kufner, A., Function Spaces, Noordhoff International Publ., Leyden, 1977.
  • Garcia-Cuerva, J., Rubio de Francia, J. L., Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, 1985.
  • Gilbarg, D., Trudinger, N. S., Elliptic Partial Equations of Second Order, 2nd Ed., Springer, New York, 1983.
  • Heinonen, J., Kilpelainen, T., Martio, O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford University Press, Inc., New York, 1993.
  • Kufner, A., Weighted Sobolev Spaces, John Wiley & Sons, 1985.
  • Muckenhoupt, B., Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
  • Talbi, M., Tsouli, N., On the spectrum of the weighted p-Biharmonic operator with weight, Mediterr. J. Math. 4 (2007), 73-86.
  • Torchinsky, A., Real-Variable Methods in Harmonic Analysis, Academic Press, San Diego, 1986.
  • Turesson, B. O., Nonlinear Potential Theory and Weighted Sobolev Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 2000.
  • Zeidler, E., Nonlinear Functional Analysis and Its Applications. Vol. I, Springer-Verlag, New York, 1990.
  • Zeidler, E., Nonlinear Functional Analysis and Its Applications. Vol. II/B, Springer-Verlag, New York, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2016_70_2_9
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