Problems of minimization for elliptic equations with non standard growth

Abstract

In the first part of this work, we deal with the Rayleigh quotient (...),(...),(...),(...) is a bounded domain of (...) and (...). Hence, we describe the asymptotic behavior of its minimizers, first when (...) and after when (...). In the second part, we prove the existence of at least one ground state solution for the semilinear elliptic equation (...), where G is either (...) or a bounded domain, (...) and (...)is a continuous function assuming critical and subcritical values.