1 |
X. L. Fan and D. Zhao, On the spaces and , J. Math. Anal. Appl. 263 (2001), no. 2, 424-446.
DOI
ScienceOn
|
2 |
X. L. Fan and Q. H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problem, Nonlinear Anal. 52 (2003), no. 8, 1843-1852.
DOI
ScienceOn
|
3 |
X. L. Fan, Q. Zhang, and D. Zhao, Eigenvalues of p(x)-Laplacian Dirichlet problem, J. Math. Anal. Appl. 302 (2005), no. 2, 306-317.
DOI
ScienceOn
|
4 |
T. C. Halsey, Electrorheological fluids, Science 258 (1992), 761-766.
DOI
ScienceOn
|
5 |
P. Harjulehto, P. Hasto, M. Koskenoja, and S. Varonen, The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values, Potential Anal. 25 (2006), no. 3, 205-222.
DOI
|
6 |
P. Hasto, The p(x)-Laplacian and applications, J. Anal. 15 (2007), 53-62.
|
7 |
E. Acerbi and G. Mingione, Regularity results for stationary electro-rheological fluids, Arch. Ration. Mech. Anal. 164 (2002), no. 3, 213-259.
DOI
|
8 |
G. A. Afrouzi, S. Mahdavi, and Z. Naghizadeh, The Nehari manifold for p-Laplacian equation with Dirichlet boundary condition, Nonlinear Anal. Model. Control 12 (2007), no. 2, 143-155.
|
9 |
A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994), no. 2, 519-543.
DOI
ScienceOn
|
10 |
K. J. Brown and Y. Zhang, The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function, J. Differential Equations 193 (2003), no. 2, 481-499.
DOI
ScienceOn
|
11 |
O. M. Buhrii and R. A. Mashiyev, Uniqueness of solutions of the parabolic variation inequality with variable exponent of nonlinearity, Nonlinear Anal. 10 (2009), 2325-2331.
|
12 |
M. Ruzicka, Electrorheological Fluids: modeling and mathematical theory, Springer Lecture Notes in Math. Vol. 1748, Springer Verlag, Berlin, Heidelberg, New York, 2000.
|
13 |
V. V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, (russian) Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986), no. 4, 675-710, 877.
|
14 |
M. Mihailescu, Existence and multiplicity of solutions for an elliptic equation with p(x)-growth conditions, Glasg. Math. J. 48 (2006), no. 3, 411-418.
DOI
ScienceOn
|
15 |
M. Mihailescu and V. Radulescu, A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462 (2006), no. 2073, 2625-2641.
DOI
ScienceOn
|
16 |
M. Mihailescu and V. Radulescu, On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent, Proc. Amer. Math. Soc. 135 (2007), no. 9, 2929-2937.
DOI
ScienceOn
|
17 |
S. Ogras, R. A. Mashiyev, M. Avci, and Z. Yucedag, Existence of solutions for a class of elliptic systems in involving the (p(x), q(x))-Laplacian, J. Inequal. Appl. 2008 (2008), Art. Id 612938, 16 pp.
|
18 |
X. Zhang and X. Liu, The local boundedness and Harnack inequality of p(x)-Laplace equation, J. Math. Anal. Appl. 332 (2007), no. 1, 209-218.
DOI
ScienceOn
|
19 |
N. S. Trudinger, On Harnack type inequalities and their application to quasilinear elliptic equations, Comm. Pure Appl. Math. 20 (1967), 721-747.
DOI
|
20 |
T. F. Wu, Multiplicity of positive solution of p-Laplacian problems with sign-changing weight functions, Int. J. Math. Anal. (Ruse) 1 (2007), no. 9-12, 557-563.
|
21 |
O. Kovacik and J. Rakosnik, On spaces and , Czechoslovak Math. J. 41(116) (1991), no. 4, 592-618.
|
22 |
R. A. Mashiyev, Some properties of variable Sobolev capacity, Taiwanese J. Math. 12 (2008), no. 3, 671-678.
DOI
|
23 |
J. Chabrowski and Y. Fu, Existence of solutions for p(x)-Laplacian problems on a bounded domain, J. Math. Anal. Appl. 306 (2005), no. 2, 604-618.
DOI
ScienceOn
|
24 |
L. Diening, Theoretical and Numerical Results for Electrorheological Fluids, Ph. D. thesis, University of Frieburg, Germany, 2002.
|
25 |
D. Edmunds and J. Rakosnik, Sobolev embeddings with variable exponent, Studia Math. 143 (2000), no. 3, 267-293.
DOI
|
26 |
A. El Hamidi, Existence results to elliptic systems with nonstandard growth conditions, J. Math. Anal. Appl. 300 (2004), no. 1, 30-42.
DOI
ScienceOn
|
27 |
X. L. Fan, Solutions for p(x)-Laplacian Dirichlet problems with singular coefficients, J. Math. Anal. Appl. 312 (2005), no. 2, 464-477.
DOI
ScienceOn
|
28 |
X. L. Fan, J. S. Shen, and D. Zhao, Sobolev embedding theorems for spaces , J. Math. Anal. Appl. 262 (2001), no. 2, 749-760.
DOI
ScienceOn
|