Extrinsic bounds for the spectrum of a Steklov problem associated with the (p,q)-Laplacian

A Steklov-like boundary problem associated with the (p, q)-Laplacian is considered in a bounded domain R n with a smooth boundary, where p, q (1, +) and p = q.It is known that the set of eigenvalues of this problem is {0} (1, +), where 1 is a positive constant.The aim of the present article is to give upper bounds for 1.These bounds are of two types: one based on the isoperimetric ratio and the other on the geometry of the boundary.Additionally, it is shown that if 1 is close to any of these upper bounds, then is close to a ball.