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On a sub-supersolution method for variational inequalities with Leray-Lions operators in variable exponent spaces. (English) Zbl 1179.35148

The author investigates a sub-supersolution method for a variational inequality
\(\int_\varOmega A(x,\nabla u)\cdot (\nabla v -\nabla u)dx+\int_\varOmega f(x,u)( v - u)dx+\int_{\partial\varOmega} g(x,u)( v - u)dS\geq 0\;\forall v\in K\),
where \(K\) is a closed subset of the Sobolev space \(W^{1,p(\cdot)}(\varOmega)\) with a variable exponent \(p(\cdot)\). Existence and qualitative properties of solutions between sub and supersolutions are established.

MSC:

35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators
35B45 A priori estimates in context of PDEs
35J20 Variational methods for second-order elliptic equations
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