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Existence of solutions and positivity of the infimum eigenvalue for degenerate elliptic equations with variable exponents

Pages: 695 - 707, Issue special, November 2013

 Abstract        References        Full Text (384.9K)          

Inbo Sim - Department of Mathematics, University of Ulsan, Ulsan 680-749, South Korea (email)
Yun-Ho Kim - Department of Mathematics Education, Sangmyung University, Seoul 110-743, South Korea (email)

1 T. Bartsch, Z. Liu, On a superlinear elliptic $p$-Laplacian equation, J. Differential Equations 198 (2004), 149-175.       
2 N. Benouhiba, On the eigenvalues of weighted $p(x)$-Laplacian on $\mathbbR^N$, Nonlinear Anal. 74 (2011), 235-243.       
3 Y. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006), 1383-1406.       
4 L. Diening, Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces $L^{p(\cdot)}$ and $W^{k,p(\cdot)}$, Math. Nachr. 268 (2004), 31-43.       
5 G. Dinca, P. Jebelean, J. Mawhin, Variational and topological methods for Dirichlet problems with $p$-Laplacian, Portugal. Math. 58 (2001), 339-378.       
6 P. Drábek, A. Kufner, F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singularities, de Gruyter, Berlin, 1997.       
7 P. De Napoli, M. Mariani, Mountain pass solutions to equations of $p$-Laplacian type, Nonlinear Anal. 54 (2003), 1205-1219.       
8 X. Fan, D. Zhao, On the spaces $L^{p(x)}(\Omega)$ and $W^{m,p(x)}(\Omega)$, J. Math. Anal. Appl. 263 (2001), 424-446.       
9 X.L. Fan, Q.H. Zhang, Existence of solutions for $p(x)$-Laplacian Dirichlet problem, Nonlinear Anal. 52 (2003), 1843-1852.       
10 X. Fan, Q. Zhang, D. Zhao, Eigenvalues of $p(x)$-Laplacian Dirichlet problem, J. Math. Anal. Appl. 302 (2005), 306-317.       
11 H. Galewski, On the continuity of the Nemyskij operator between the spaces $L^{p_1(x)}$ and $L^{p_2(x)}$, Georgian Math. Journal. 13 (2006), 261-265.       
12 P. Harjulehto, Variable exponent Sobolev spaces with zero boundary values, Math. Bohem. 132 (2007), 125-136.       
13 Y. Huang, Existence of positive solutions for a class of the $p$-Laplace equations, J. Austral. Math. Soc. Sect. B 36 (1994), 249-264.       
14 Y.-H. Kim, L. Wang, C. Zhang, Global bifurcation for a class of degenerate elliptic equations with variable exponents, J. Math. Anal. Appl. 371 (2010), 624-637.       
15 O. Kováčik, J. Rákosník, On spaces $L^{p(x)}$ and $W^{k,p(x)}$, Czechoslovak Math. J. 41 (1991), 592-618.       
16 J. Musielak, Orlicz spaces and modular spaces, Springer-Verlag, Berlin, 1983.       
17 K. Rajagopal, M. R.užička, Mathematical modeling of electrorheological materials, Continuum Mech. Thermodyn. 13 (2001), 59-78.
18 M. R.užička, Electrorheological Fluids: Modeling and Mathematical Theory, in: Lecture Notes in Mathematics, vol. 1748, Springer, Berlin, 2000.       
19 A. Szulkin, M.Willem, Eigenvalue problem with indefinite weight, Studia Math. 135 (1995), 191-201.       
20 M. Willem, Minimax Theorems, Birkhauser, Basel, 1996.       
21 V.V. Zhikov, On some variational problems, Russ. J. Math. Phys. 5 (1997), 105-116.       
22 V.V. Zhikov, On the density of smooth functions in Sobolev-Orlicz spaces, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 226 (2004), 67-81.       

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