{ "id": "1403.3149", "version": "v1", "published": "2014-03-13T02:39:59.000Z", "updated": "2014-03-13T02:39:59.000Z", "title": "Existence, Uniqueness of Positive Solution to a Fractional Laplacians with Singular Nonlinearity", "authors": [ "Yanqin Fang" ], "comment": "In this paper we deal with the fractional Laplacian with singular nonlinearity. We prove the existence and uniqueness of the solution to this kind of equations. Although the nonlinearity is singular, we obtain the regularity of the solution. In order to derive existence of solution, we employ the method of sub- and supersolutions", "categories": [ "math.AP" ], "abstract": "In this paper we prove the existence and uniqueness of positive classical solution of the fractional Laplacian with singular nonlinearity in a smooth bounded domain with zero Drichlet boundary conditions. By the method of sub-supersolution, we derive the existence of positive classical solution to the approximation problems. In order to obtain the regularity, we first establish the existence of weak solution for the fraction Laplacian. Thanks to \\cite{XY}, the regularity follows from the boundedness of weak solution.", "revisions": [ { "version": "v1", "updated": "2014-03-13T02:39:59.000Z" } ], "analyses": { "subjects": [ "35J25", "47G30" ], "keywords": [ "fractional laplacian", "singular nonlinearity", "positive solution", "uniqueness", "weak solution" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2014arXiv1403.3149F" } } }