非线性分数阶拉普拉斯问题的正解

IF 0.8 4区数学 Q2 MATHEMATICS

Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI:10.58997/ejde.sp.02.h1

Elliott Hollifield

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引用次数: 0

摘要

考虑一类非线性分数阶拉普拉斯问题在有界域外满足齐次狄利克雷条件。证明了一类在无穷远处为次线性或渐近线性的非线性问题的正弱解的存在性。我们用分解和超解的方法来建立结果。本文还利用一维有限元方法给出了与理论结果相对应的数值分岔图。参见https://ejde.math.txstate.edu/special/02/h1/abstr.html

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Positive solutions for nonlinear fractional Laplacian problems

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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来源期刊

Electronic Journal of Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

3 months

期刊介绍： All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.