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Existence results to elliptic systems with nonstandard growth conditions. (English) Zbl 1148.35316

Summary: Nonstandard growth conditions in partial differential equations have been the subject of recent developments in elastic mechanics and electrorheological fluid dynamics [M. Ruzicka, Electrorheological fluids: modeling and mathematical theory. Lecture Notes in Mathematics, 1748. Berlin: Springer-Verlag (2000; Zbl 0962.76001); C. R. Acad. Sci., Paris, Sér. I, Math. 329, No. 5, 393–398 (1999; Zbl 0954.76097); V. V. Zhikov, Math. USSR, Izv. 29, 33–66 (1987), translation from Izv. Akad. Nauk SSSR Ser. Mat. 50, No. 4, 675–710 (1986; Zbl 0599.49031)].
In this work, elliptic systems with nonstandard growth conditions are studied. Existence and multiplicity results, under growth conditions on the reaction terms, are established.

MSC:

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35J60 Nonlinear elliptic equations
47J30 Variational methods involving nonlinear operators
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