Abstract
This paper deals with a class of the stationary nonlinear Schrödinger
Systems in
References
[1] E. Acerbi and G. Mingione, Regularity results for a class of functionals with non-standard growth, Arch. Ration. Mech. Anal. 156 (2001), no. 2, 121–140. 10.1007/s002050100117Search in Google Scholar
[2]
G. A. Afrouzi and S. Heidarkhani,
Existence of three solutions for a class of Dirichlet quasilinear elliptic systems involving the
[3] C. O. Alves, Existence of positive solutions for a problem with lack of compactness involving the p-Laplacian, Nonlinear Anal. 51 (2002), no. 7, 1187–1206. 10.1016/S0362-546X(01)00887-2Search in Google Scholar
[4]
C. O. Alves,
Existence of solution for a degenerate
[5]
C. O. Alves,
Existence of radial solutions for a class of
[6]
C. O. Alves and M. A. S. Souto,
Existence of solutions for a class of problems in
[7] H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), no. 4, 437–477. 10.1002/cpa.3160360405Search in Google Scholar
[8] L. Diening, P. Harjulehto, P. Hästö and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Springer, Berlin, 2010. 10.1007/978-3-642-18363-8Search in Google Scholar
[9]
A. Djellit and S. Tas,
Existence of solutions for a class of elliptic systems in
[10]
A. Djellit, Z. Youbi and S. Tas,
Existence of solutions for elliptic systems in
[11] D. E. Edmunds and J. Rákosník, Sobolev embeddings with variable exponent, Studia Math. 143 (2000), no. 3, 267–293. 10.4064/sm-143-3-267-293Search in Google Scholar
[12] I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324–353. 10.1016/0022-247X(74)90025-0Search in Google Scholar
[13] A. El Hamidi, Existence results to elliptic systems with nonstandard growth conditions, J. Math. Anal. Appl. 300 (2004), no. 1, 30–42. 10.1016/j.jmaa.2004.05.041Search in Google Scholar
[14]
X. Fan, J. S. Shen and D. Zhao,
Sobolev embedding theorems for spaces
[15]
X. Fan, Q. Zhang and D. Zhao,
Eigenvalues of
[16]
X. Fan and D. Zhao,
On the spaces
[17]
X. Fan, Y. Zhao and D. Zhao,
Compact imbedding theorems with symmetry of Strauss-Lions type for the space
[18] O. Kavian, Introduction à la théorie des points critiques et applications aux problèmes elliptiques, Math. Appl. (Berlin) 13, Springer, Paris, 1993. Search in Google Scholar
[19] A. Kristály, Existence of two non-trivial solutions for a class of quasilinear elliptic variational systems on strip-like domains, Proc. Edinb. Math. Soc. (2) 48 (2005), no. 2, 465–477. 10.1017/S0013091504000112Search in Google Scholar
[20] P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 4, 223–283. 10.1016/S0294-1449(16)30422-XSearch in Google Scholar
[21]
S. Ogras, R. A. Mashiyev, M. Avci and Z. Yucedag,
Existence of solutions for a class of elliptic systems in
[22] M. Růžička, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math. 1748, Springer, Berlin, 2000. 10.1007/BFb0104029Search in Google Scholar
[23] M. Struwe, Variational Methods, 2nd ed., Ergeb. Math. Grenzgeb. (3) 34, Springer, Berlin, 1996. 10.1007/978-3-662-03212-1Search in Google Scholar
[24] S. Tas, Etude de Systèmes elliptiques non linéaires, Ph.D. thesis, University of Annaba, Algeria, 2002. Search in Google Scholar
[25] M. Willem, Minimax Theorems, Progr. Nonlinear Differential Equations Appl. 24, Birkhäuser, Boston, 1996. 10.1007/978-1-4612-4146-1Search in Google Scholar
[26]
X. Xu and Y. An,
Existence and multiplicity of solutions for elliptic systems with nonstandard growth condition in
[27]
H. Yin and Z. Yang,
Three solutions for a class of quasilinear elliptic systems involving the
[28] E. Zeidler, Nonlinear Functional Analysis and its Applications. II/B, Springer, New York, 1990. 10.1007/978-1-4612-0981-2Search in Google Scholar
[29]
Q. Zhang,
Existence of radial solutions for
[30] W. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Math USSR Izv. 29 (1987), 33–66. 10.1070/IM1987v029n01ABEH000958Search in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston