Abstract
This paper is concerned with the study of the nonlinear elliptic
equations in a bounded subset Ω ⊂ RN Au = f, where A is an operator of
Leray-Lions type acted from the space W1,p(·)0(Ω) into its dual. when
the second term f belongs to Lm(·), with m(·) > 1 being
small. we prove existence and regularity of weak solutions for this
class of problems p(x)-growth conditions. The functional framework
involves Sobolev spaces with variable exponents as well as Lebesgue
spaces with variable exponents.