Essentials of Nonlocal Operators

Bucur, Claudiu B.

doi:10.1515/9783110571561-002

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2023

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“…This characterization allowed them to prove several regularity results by using local techniques and provides a framework for interested researchers to further the study of the still emerging field of fractional Laplacian problems. Since then, the progress has been swift and there are already several excellent survey papers and monographs available, see [2,5,6,13,20,23,26,27,33] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Positive solutions for nonlinear fractional Laplacian problems

Hollifield

2023

ejde

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We consider a class of nonlinear fractional Laplacian problems satisfying the homogeneous Dirichlet condition on the exterior of a bounded domain. We prove the existence of a positive weak solution for classes of nonlinearities which are either sublinear or asymptotically linear at infinity. We use the method of sub-and-supersolutions to establish the results. We also provide numerical bifurcation diagrams, corresponding to the theoretical results, using the finite element method in one dimension. See also https://ejde.math.txstate.edu/special/02/h1/abstr.html

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