Existence of positive solutions for fractional Laplacian equations: theory and numerical experiments
Date
2020-07-28
Authors
Chhetri, Maya
Girg, Petr
Hollifield, Elliott
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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 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.
Description
Keywords
Fractional Laplacian, Sub- and supersolution, Sublinear, Logistic equation, Finite element method
Citation
Chhetri, 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.
Rights
Attribution 4.0 International