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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2004 | 83 | 1 | 65-76

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

EN

### Abstrakty

EN
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 $𝓒_L(ℝⁿ₊)$ of all positive L-solutions continuously vanishing on the boundary {xₙ = 0}.

65-76

wydano
2004

### Twórcy

autor
• Department of Mathematics, Faculty of Sciences of Tunis, Campus Universitaire, 1060 Tunis, Tunisia
autor
• Department of Mathematics, Faculty of Sciences of Tunis, Campus Universitaire, 1060 Tunis, Tunisia