Existence of positive solutions for fractional Laplacian equations: theory and numerical experiments

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dc.contributor.authorChhetri, Maya
dc.contributor.authorGirg, Petr
dc.contributor.authorHollifield, Elliott
dc.date.accessioned2021-10-04T14:30:36Z
dc.date.available2021-10-04T14:30:36Z
dc.date.issued2020-07-28
dc.description.abstractWe 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 positive weak solution for classes of sublinear nonlinearities including logistic type. A method of sub- and supersolution, without monotone iteration, is established to prove our existence results. We also provide numerical bifurcation diagrams and the profile of positive solutions, corresponding to the theoretical results using the finite element method in one dimension.
dc.description.departmentMathematics
dc.formatText
dc.format.extent31 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationChhetri, M., Girg, P., & Hollifield, E. (2020). Existence of positive solutions for fractional Laplacian equations: theory and numerical experiments. <i>Electronic Journal of Differential Equations, 2020</i>(81), pp. 1-31.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14588
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectFractional Laplacian
dc.subjectSub- and supersolution
dc.subjectSublinear
dc.subjectLogistic equation
dc.subjectFinite element method
dc.titleExistence of positive solutions for fractional Laplacian equations: theory and numerical experiments
dc.typeArticle

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