Chhetri, MayaGirg, PetrHollifield, Elliott2021-10-042021-10-042020-07-28Chhetri, 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. 1-31.1072-6691https://hdl.handle.net/10877/14588We 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.Text31 pages1 file (.pdf)enAttribution 4.0 InternationalFractional LaplacianSub- and supersolutionSublinearLogistic equationFinite element methodArticle