Resolvents in semi-linear harmonic spaces (Q1977858)

The author studies potential kernels that are defined in the context of semi-linear harmonic spaces. Semi-linear harmonic spaces are obtained by semi-linear perturbation of linear harmonic spaces. Let \(^SV\) be a semi-linear potential kernel. There is a nonlinear resolvent associated with \(^SV\). This resolvent is defined by \(^SV_\lambda^SV(I+\lambda^SV)^{-1}\) and there is a constant \(C<\infty\) with \(\|\lambda V_\lambda\|^L\leq C\) for all \(\lambda>0\). Furthermore, the bounded excessive functions of this resolvent correspond to the bounded hyperharmonic functions as they do in linear potential theory.