AN ELLIPTIC BOUNDARY VALUE PROBLEM WITH FRACTIONAL NONLINEARITY
SIAM JOURNAL ON MATHEMATICAL ANALYSIS(2021)
摘要
We investigate the existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the nonexistence regimes. For the existence results, we make use of a particular class of weighted Sobolev spaces to compensate for boundary singularities which are naturally built in the problem.
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关键词
Dirichlet problem,operators of mixed order,comparison principles,fixed-point arguments,large solutions
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