Existence results to elliptic systems with nonstandard growth conditions

Nonstandard growth conditions in partial differential equations have been the subject of recent developments in elastic mechanics and electrorheological fluid dynamics [Lecture Notes in Mathematics, vol. 1748, 2000; C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 393–398; Math. USSR Izv. 29 (1987) 33–66]. In this work, elliptic systems with nonstandard growth conditions are studied. Existence and multiplicity results, under growth conditions on the reaction terms, are established.  2004 Elsevier Inc. All rights reserved.