We consider the general Schrödinger operator on a half-space in ℝⁿ, n ≥ 3. We prove that the L-Green function G exists and is comparable to the Laplace-Green function provided that μ is in some class of signed Radon measures. The result extends the one proved on the half-plane in [9] and covers the case of Schrödinger operators with potentials in the Kato class at infinity considered by Zhao and Pinchover. As an application we study the cone of all positive L-solutions continuously vanishing on the boundary xₙ = 0.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-8,
author = {Abdoul Ifra and Lotfi Riahi},
title = {On the equivalence of Green functions for general Schr\"odinger operators on a half-space},
journal = {Annales Polonici Mathematici},
volume = {83},
year = {2004},
pages = {65-76},
zbl = {1061.31006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-8}
}
Abdoul Ifra; Lotfi Riahi. On the equivalence of Green functions for general Schrödinger operators on a half-space. Annales Polonici Mathematici, Tome 83 (2004) pp. 65-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-8/