Bounded positive solutions for diffusive logistic equations with unbounded distributed limitations-Reference-Cited by-同舟云学术

Bounded positive solutions for diffusive logistic equations with unbounded distributed limitations

Published:2022 Issue:10 Volume:15 Page:2871
ISSN:1937-1632
Container-title:Discrete and Continuous Dynamical Systems - S
language:
Short-container-title:DCDS-S

Author:

Díaz Jesús Ildefonso¹,Hernández Jesús¹

Affiliation:

1. Instituto Matemático Interdisplinar, Depto. Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain

Abstract

<p style='text-indent:20px;'>We establish the existence of bounded very weak solutions to a large class of stationary diffusive logistic equations with weights by constructing suitable sub and supersolutions. This class of problems corresponds to the case in which the absorption term dominates over the forcing term. The case of simultaneous singular nonlinearities and singular weights is also considered. This shows that if limitations in the growth of a population are distributed and unbounded, but satisfy some mild integrability assumption in terms of the distance to the boundary, solutions can still be bounded. The results extend several papers in the literature.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference41 articles.

1. M. Bertsch, R. Rostamian.The principle of linearized stability for a class of degenerate diffusion equations, J. Differ. Equat., 57 (1985), 373-405.

2. L. Boccardo and L. Orsina, Sublinear elliptic equations in $L^{s}$, Houston J. Math., 20 (1994), 99–114.

3. L. Boccardo and L. Orsina, Semilinear elliptic equations with singular nonlinearities, Calc. Var. Partial Differential Equations, 37 (2010), 363–380.

4. H. Brezis and F. E. Browder, Some properties of higher order Sobolev spaces, J. Math. Pures Appl., 61 (1982), 245–259.

5. H. Brezis and X. Cabré, Some simple nonlinear PDE's without solutions, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat., 1 (1998), 223–262.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The logistic problem with nonlinear directed advection;Nonlinear Analysis: Real World Applications;2024-04

2. Multiple principal eigenvalues for indefinite quasilinear problems;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2022-11-21