POSITIVE SOLUTIONS FOR NONLINEAR FRACTIONAL LAPLACIAN PROBLEMS

被引：0
|
作者：
Hollifield, Elliott [1 ]
机构：
[1] Univ N Carolina, Pembroke, NC 28372 USA
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年
关键词：
Fractional Laplacian; sublinear; asymptotically linear; sub- and supersolution; positive weak solution; EXTENSION PROBLEM;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：135 / 149
页数：15
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