The Malgrange-Ehrenpreis theorem for nonlocal Schrödinger operators with certain potentials

2016/12/15 by Woocheol Choi, Choi, Woocheol, Yong-Cheol Kim +1
Mathematics · #35B65 #35D10 (60J75) #35J60 #45K05 #47G20 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.AP #math.CA #msc:35B65 #msc:35D10 #msc:35J60 #msc:45K05 #msc:47G20

paper · pdf · doi:10.48550/arxiv.1612.07143

arxiv created 2016/12/15 · arxiv updated 2016/12/22

Abstract

In this paper, we prove the Malgrange-Ehrenpreis theorem for nonlocal Schrödinger operators L_K+V with nonnegative potentials V∈ L^q_\loc(\BRⁿ) for q>\fn2s with 0<s<1 and n≥ 2; that is to say, we obtain the existence of a fundamental solution \fe_V for L_K+V satisfying (L_K+V)\fe_V=\dt₀ in \BRⁿ in the distribution sense, where \dt₀ denotes the Dirac delta mass at the origin. In addition, we obtain a decay of the fundamental solution \fe_V.

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