Existence and non-existence results for a semilinear fractional Neumann problem

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Nodea-Nonlinear Differential Equations and Applications Pub Date : 2023-10-03 DOI:10.1007/s00030-023-00886-4

Eleonora Cinti, Francesca Colasuonno

引用次数: 1

Abstract

Abstract We establish a priori $$L^\infty $$ L ∞ -estimates for non-negative solutions of a semilinear nonlocal Neumann problem. As a consequence of these estimates, we get non-existence of non-constant solutions under suitable assumptions on the diffusion coefficient and on the nonlinearity. Moreover, we prove an existence result for radial, radially non-decreasing solutions in the case of a possible supercritical nonlinearity, extending to the case $$0 0 < s ≤ 1 / 2 the analysis started in [7].

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一类半线性分数阶Neumann问题的存在性与不存在性结果

摘要建立了一类半线性非局部Neumann问题非负解的先验$$L^\infty $$ L∞估计。根据这些估计，在适当的扩散系数和非线性假设下，我们得到了非常解的不存在性。此外，我们证明了在可能的超临界非线性情况下径向非递减解的存在性结果，并推广到$$0<s\le 1/2$$ 0 ＆lt;S≤1 / 2，从[7]开始分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nodea-Nonlinear Differential Equations and Applications 数学-应用数学

CiteScore

1.70

自引率

8.30%

发文量

审稿时长

>12 weeks

期刊介绍： Nonlinear Differential Equations and Applications (NoDEA) provides a forum for research contributions on nonlinear differential equations motivated by application to applied sciences. The research areas of interest for NoDEA include, but are not limited to: deterministic and stochastic ordinary and partial differential equations, finite and infinite-dimensional dynamical systems, qualitative analysis of solutions, variational, topological and viscosity methods, mathematical control theory, complex dynamics and pattern formation, approximation and numerical aspects.