References
- Acerbi , E and Mingione , G . 2002 . Regularity results for stationary electrorheological fluids . Arch. Ration. Mech. Anal. , 164 : 213 – 259 .
- Fan , XL . 2005 . Solutions for p(x)-Laplacian Dirichlet problems with singular coefficients . J. Math. Anal. Appl. , 312 : 464 – 477 .
- Fan , XL and Zhang , QH . 2003 . Existence of solutions for p(x)-Laplacian Dirichlet problems . Nonlinear Anal. , 52 : 1843 – 1852 .
- Diening , L . 2002 . “ Theoretical and Numerical Results for Electrorheological Fluids ” . In Ph.D. thesis , University of Frieburg .
- Halsey , TC . 1992 . Electrorheological fluids . Science , 258 : 761 – 766 .
- Mihăilescu , M and Rădulescu , V . 2006 . A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids . Proc. R. Soc. A , 462 : 2625 – 2641 .
- Mihăilescu , M and Rădulescu , V . 2007 . On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent . Proc. Am. Math. Soc. , 135 ( 9 ) : 2929 – 2937 .
- Růžička , M . 2000 . Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics , Vol. 1748 , Berlin : Springer-Verlag .
- Zhikov , VV . 1986 . Averaging of functionals of the calculus of variations and elasticity theory . Izv. Akad. Nauk SSSR Ser. Mat. , 50 : 675 – 710 . (in Russian)
- Harjulehto , P , Hästö , P , Lê , Út.V. and Nuortio , M . 2010 . Overview of differential equations with non-standard growth . Nonlinear Anal. , 72 : 4551 – 4574 .
- Orlicz , W . 1931 . Über konjugierte Exponentenfolgen . Stud. Math. , 3 : 200 – 212 .
- Nakano , H . 1950 . Modulared Semi-ordered Linear Spaces , Tokyo : Maruzen .
- Hästö , P . 2007 . The p(x)-Laplacian and applications . J. Anal. , 15 : 53 – 62 . (Special proceedings volume)
- Duc , DM and Vu , NT . 2005 . Nonuniformly elliptic equations of p-Laplacian type . Nonlinear Anal. , 61 : 1483 – 1495 .
- Vu , NT . 2005 . Mountain pass theorem and nonuniformly elliptic equations . Vietnam J. Math. , 33 ( 4 ) : 391 – 408 .
- Duc , DM . 1989 . Nonlinear singular elliptic equations . J. London Math. Soc. , 40 ( 2 ) : 420 – 440 .
- Toan , HQ and Ngô , QA . 2009 . Multiplicity of weak solutions for a class of nonuniformly elliptic equations of p-Laplacian type . Nonlinear Anal. , 70 ( 4 ) : 1536 – 1546 .
- Edmunds , D and Rakosnik , J . 2000 . Sobolev embeddings with variable exponent . Stud. Math. , 143 : 267 – 293 .
- Fan , XL , Shen , JS and Zhao , D . 2001 . Sobolev embedding theorems for spaces W k,p(x)(Ω) . J. Math. Anal. Appl. , 262 : 749 – 760 .
- Fan , XL and Zhao , D . 2001 . On the spaces L p(x)(Ω) and W m,p(x)(Ω) . J. Math. Anal. Appl. , 263 : 424 – 446 .
- Kovăčik , O and Răkosnik , J . 1991 . On spaces L p(x) and W k,p(x) . Czechoslovak Math. J. , 41 : 592 – 618 .
- Samko , S . 1998 . Convolution type operators in L p(x) . Integr. Transform. Special Funct. , 7 : 123 – 144 .
- S. Samko, Denseness of in the generalized Sobolev spaces W m,p(x)(R N ), Int. Soc. pp. 333–342 in Direct and Inverse Problems of Mathematical Physics (Newark, DE, 1997), Int. Soc. Anal. Appl. Comput. 5, Kluwer Acad. Publ., Dordrecht, 2000
- Brezis , H . 1992 . Analyse Fonctionnelle. Théorie, Méthodes et Applications , Paris : Masson .
- Willem , M . 1996 . Minimax Theorems , Basel : Birkhauser .
- Mashiyev , RA , Ogras , S , Yucedag , Z and Avci , M . 2010 . The Nehari manifold approach for Dirichlet problem involving the p(x)-Laplacian equation . J. Korean Math. Soc. , 47 ( 4 ) : 845 – 860 .
- Ekeland , I . 1974 . On the variational principle . J. Math. Anal. Appl. , 47 : 324 – 353 .