Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent

• Stanislas Ouaro ^[1]
  1. [1] University of Ouagadougou

     University of Ouagadougou

     Burkina Faso

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 14, Nº. 2, 2012, págs. 15-41
• Idioma: inglés
• DOI: 10.4067/S0719-06462012000200002
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• Referencias bibliográficas
  • Alvino, A,Boccardo, L,Ferone, V,Orsina, L,Trombetti, G. (2003). Existence results for non-linear elliptic equations with degenerate coercivity....
  • Andreu, F,Igbida, N,Mazón, J.M,Toledo, J. (2007). existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary...
  • Andreu, F,Mazón, J. M,Segura De Leon, S,Toledo, J. (1997). Quasi-linear elliptic and parabolic equations in with nonlinear boundary conditions....
  • Antontsev, S.N,Rodrigues, J.F. (2006). On stationary thermo-rheological viscous flows. Annal del Univ de Ferrara. 52. 19-36
  • Bénilan, P,Boccardo, L,Gallouét, T,Gariepy, R,Pierre, M,Vazquez, J.L. (1995). An theory of existence and uniqueness of nonlinear elliptic...
  • Brezis, H. (1983). Analyse Fonctionnelle: Theorie et Applications. Masson. Paris.
  • Chen, Y,Levine, S,Rao, M. (2006). Variable exponent: linear growth functionals in image restoration. SIAM. J.Appl. Math. 66. 1383-1406
  • Diening, L. (2004). Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces and. Math. Nachr. 268. 31-43
  • Diening, L. (2002). Theoretical and numerical results for electrorheological fluids.
  • Edmunds, D. E,Rakosnik, J. (1992). Density of smooth functions in. Proc. R. Soc. A. 437. 229-236
  • Edmunds, D. E,Rakosnik, J. (2000). Sobolev embeddings with variable exponent. Sudia Math. 143. 267-293
  • Edmunds, D. E,Rakosnik, J. (2002). Sobolev embeddings with variable exponent, II. Math. Nachr. 246247. 53-67
  • Fan, X,Deng, S. (2009). Multiplicity of Positive Solutions for a Class of Inhomogeneous Neumann Problems Involving the Laplacian. Nonlinear...
  • Fan, X,Zhang, Q. (2003). Existence of solutions for Laplacian Dirichlet problem. Nonlinear Anal. 52. 1843-1852
  • Fan, X,Zhao, D. (2001). On the spaces and. J. Math. Anal. Appl. 263. 424-446
  • Halmos, P. (1950). Measure Theory. D. Van Nostrand. New York.
  • Kovacik, O,Rakosnik, J. (1991). On spaces and. Czech. Math. J. 41. 592-618
  • Krasnosel'skii, M. (1964). Topological methods in the theory of nonlinear integral equations. Perga-mon Press. New York.
  • Mihailescu, M,Radulescu, V. (2006). A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids....
  • Morrey, C. B. Jr. (1966). Multiple Intóegrals in the Calculus of Variations. Springer-Verlag.
  • Musielak, J. (1983). Orlicz Spaces and modular spaces: Lecture Notes in Mathematics. springer. Berlin.
  • Nakano, H. (1950). Modulared semi-ordered linear spaces. Maruzen Co., Ltd. Tokyo.
  • Necas, J. (1967). Les móethodes Directes en Thóeorie des Equations Elliptiques. Masson et Cie. Paris.
  • Ouaro, S,Soma, S. (2011). Weak and entropy solutions to nonlinear Neumann boundary value problem with variable exponent. Complex var. Elliptic...
  • Ouaro, S,Traoré, S. (2010). Existence and uniqueness of entropy solutions to nonlinear elliptic problems with variable growth. Int. J. Evol....
  • Ouaro, S,Traoré, S. (2009). Weak and entropy solutions to nonlinear elliptic problems with variable exponent. J. Convex Anal. 16. 523-541
  • Rajagopal, K.R,Ruzicka, M. (2001). Mathematical Modeling of Electrorheological Materials. Contin. Mech. Thermodyn. 13. 59-78
  • Ricceri, B. (2000). On three critical points theorem. Arch. Math. 75. 220-226
  • Ruzicka, M. (2002). Electrorheological fluids: modelling and mathematical theory, Lecture Notes in Mathematics 1748. Springer-Verlag. Berlin....
  • Sanchon, M,Urbano, J. M. (2009). Entropy solutions for the Laplace Equation. Trans. Amer. Math. Soc. 361. 6387-6405
  • Sharapudinov, I. (1978). On the topology of the space. Math. Zametki. 26. 613-632
  • Tsenov, I. (1961). Generalization of the problem of best approximation of a function in the space. Uch. Zap. Dagestan Gos. Univ. 7. 25-37
  • Wang, L,Fan, Y,Ge, W. (2009). Existence and multiplicity of solutions for a Neumann problem involving the Laplace operator. Nonlinear Anal....
  • Yao, J. (2008). Solutions for Neumann boundary value problems involving p(x)-Laplace operators. Nonlinear Anal. 68. 1271-1283
  • Zhikov, V. (1992). On passing to the limit in nonlinear variational problem. Math. Sb. 183. 47-84