It is well known that strong Feller semigroups generate balayage spaces provided the set of their excessive functions contains sufficiently many elements. In this note, we give explicit examples of strong Feller semigroups which do generate balayage spaces. Further we want to point out the role of the generator of the semigroup in the related potential theory.

We study the sequence $u_n$, which is solution of $-div\left(a(x,𝔻u_n)\right)+{\Phi }^{\text{'}\text{'}}\left(\right|u_n\left|\right)u_n=f_n+g_n$ in $\Omega$ an open bounded set of ${𝐑}^N$ and $u_n=0$ on $\partial \Omega$, when $f_n$ tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the $N$-function $\Phi$, and prove a non-existence result.

We study the sequence un, which is solution of $-\mathrm{div}\left(a(x,\nabla u_n)\right)+{\Phi }^{\text{'}\text{'}}\left(\right|u_n\left|\right)u_n=f_n+g_n$ in Ω an open bounded set of RN and un= 0 on ∂Ω, when fn tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the N-function Φ, and prove a non-existence result.