# On the equivalence of Green functions for general Schrödinger operators on a half-space

Annales Polonici Mathematici (2004)

- Volume: 83, Issue: 1, page 65-76
- ISSN: 0066-2216

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topAbdoul Ifra, and Lotfi Riahi. "On the equivalence of Green functions for general Schrödinger operators on a half-space." Annales Polonici Mathematici 83.1 (2004): 65-76. <http://eudml.org/doc/280911>.

@article{AbdoulIfra2004,

abstract = {We consider the general Schrödinger operator $L = div(A(x)∇_x) - μ$ 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 $G_\{Δ\}$ 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 $Kₙ^\{∞\}$ considered by Zhao and Pinchover. As an application we study the cone $_L(ℝⁿ₊)$ of all positive L-solutions continuously vanishing on the boundary xₙ = 0.},

author = {Abdoul Ifra, Lotfi Riahi},

journal = {Annales Polonici Mathematici},

keywords = {Green function; positive solution; Schrödinger operator},

language = {eng},

number = {1},

pages = {65-76},

title = {On the equivalence of Green functions for general Schrödinger operators on a half-space},

url = {http://eudml.org/doc/280911},

volume = {83},

year = {2004},

}

TY - JOUR

AU - Abdoul Ifra

AU - Lotfi Riahi

TI - On the equivalence of Green functions for general Schrödinger operators on a half-space

JO - Annales Polonici Mathematici

PY - 2004

VL - 83

IS - 1

SP - 65

EP - 76

AB - We consider the general Schrödinger operator $L = div(A(x)∇_x) - μ$ 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 $G_{Δ}$ 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 $Kₙ^{∞}$ considered by Zhao and Pinchover. As an application we study the cone $_L(ℝⁿ₊)$ of all positive L-solutions continuously vanishing on the boundary xₙ = 0.

LA - eng

KW - Green function; positive solution; Schrödinger operator

UR - http://eudml.org/doc/280911

ER -

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