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equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions","{\"arxiv\":\"1111.0796\",\"openalex\":\"W2044837570\",\"doi\":\"10.1090/s0002-9947-2014-05906-0\"}","2026-05-22T08:02:39.465143709","2026-05-22T08:02:39.465145343","doi","10.1090/s0002-9947-2014-05906-0","arxivId","1111.0796","openalexId","W2044837570","abstractText","This paper, which is the follow-up to part I, concerns the equation ( − Δ ) s v + G ′ ( v ) = 0 (-\\Delta )^{s} v+G’(v)=0 in R n \\mathbb {R}^{n} , with s ∈ ( 0 , 1 ) s\\in (0,1) , where ( − Δ ) s (-\\Delta )^{s} stands for the fractional Laplacian—the infinitesimal generator of a Lévy process. When n = 1 n=1 , we prove that there exists a layer solution of the equation (i.e., an increasing solution with limits ± 1 \\pm 1 at ± ∞ \\pm \\infty ) if and only if the potential G G has only two absolute minima in [ − 1 , 1 ] [-1,1] , located at ± 1 \\pm 1 and satisfying

Xavier Cabré 人物

Xavier Cabré · 相关文章