Existence of solution for Dirichlet problem with p(x)-Laplacien
DOI:
https://doi.org/10.5269/bspm.v33i2.24210Keywords:
p(x)-Laplacien, Generalized Lebesgue (Sobolev) spaces, Critical pointsAbstract
In this paper we study an elliptic equation involving the p(x)-Laplacien operateur, for that equation we prove the existence of a non trivial weak solution. The proof relies on simple variational arguments based on the Mountain-Pass theorem.References
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2. X. Fan, J.Shen and D. Zhao, Sobolev Embedding Theorems for Spaces Wk,p(x) (Ω), J. Math. Anal. Appl. 262(2001), 749-760.
3. X. Fan and D. Zhao, on the spaces Lp(x) (Ω) and W m,p(x) (Ω). J.Math. Anal. Appl. 263(2001), 424-446.
4. X. L.Fan and Q.H.Zhang, Existence of solution for p(x)-Laplacian Dirichlet problem. Nonlinear Anal. 52(2003), 1843-1852.
5. T. C. Halsey, Electrorheologicalfluids, Science 258(1992), 761-766.
6. P. S. Ilyas, Dirichlet problem with p(x)-Laplacian. AMS.Math.Reports 10(60),1(2008), p 43-56.
7. K. Kefi, p(x)-Laplacian with indefinite weight. AMS. V 139, N 12 (2011),p 4351-4360.
8. M. Mihailescu and V. Radulescu, A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids, Proc. Roy. Soc. London Ser. A 462(2006), 2625-2641.
9. M. Magdalena Boureanu, Existence of solution for an elliptic equation involving the p(x)- Lplace operator. E,J,D,E, Vol 2006(2006), N. 97, p. 1-10.
10. M. Ruzicka, Eletrorheological Fluids: Modeling and Mathematical Theory, Springer-Verlag, Berlin, 2002.
11. V. Zhikov, Averaging of functionals in the calculus of variations and elasticity, Math. USSR. Izv. 29(1987), 33-66.
12. D. Zhao and X. L. Fan, On the Nemytskii operators from L p1(x) (Ω) to L p2(x) (Ω). J. Lanzhou Univ. 34(1998), 1-5.
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2014-09-22
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