REGULARIZING EFFECT IN SINGULAR SEMILINEAR PROBLEMS-Reference-Cited by-同舟云学术

REGULARIZING EFFECT IN SINGULAR SEMILINEAR PROBLEMS

Published:2023-10-20 Issue:4 Volume:28 Page:561-580
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Carmona José¹^ORCID,Aparicio Antonio J. Martínez¹^ORCID,Martínez-Aparicio Pedro J. Martínez-Aparicio¹,Martínez-Teruel Miguel²^ORCID

Affiliation:

1. Departamento de Matemáticas, Universidad de Almería, Ctra. Sacramento s/n, La Cañada de San Urbano, 04120 Almería, Spain

2. Departamento de Análisis Matemático, Universidad de Granada, Avda. Fuentenueva s/n, Granada, 18071 Granada, Spain

Abstract

We analyze how different relations in the lower order terms lead to the same regularizing effect on singular problems whose model is in Ω, u = 0 on ∂Ω, where Ω is a bounded open set of is a nonnegative function in L1(Ω) and g(x,s) is a Carathéodory function. In a framework where no solution is expected, we prove its existence (regularizing effect) whenever the datum f interacts conveniently either with the boundary of the domain or with the lower order term.

Publisher

Vilnius Gediminas Technical University

Subject

Modeling and Simulation,Analysis

Reference18 articles.

1. D. Arcoya and L. Boccardo. Regularizing effect of the interplay between coefficients in some elliptic equations. J. Funct. Anal., 268(5):1153-1166, 2015. https://doi.org/10.1016/j.jfa.2014.11.011

2. D. Arcoya and L. Moreno-Mérida. Multiplicity of solutions for a Dirichlet problem with a strongly singular nonlinearity. Nonlinear Anal., 95:281-291, 2014. https://doi.org/10.1016/j.na.2013.09.002

3. L. Boccardo, S. Buccheri and C.A. dos Santos. An elliptic system with singular nonlinearities: existence via non variational arguments. J. Math. Anal. Appl., 516(1):Paper No. 126490, 21 pp., 2022. https://doi.org/10.1016/j.jmaa.2022.126490

4. L. Boccardo and L. Orsina. Semilinear elliptic equations with singular nonlinearities. Calc. Var. Partial Differential Equations, 37(3-4):363-380, 2010. https://doi.org/10.1007/s00526-009-0266-x

5. J. Carmona, T. Leonori, S. López-Martínez and P.J. Martínez-Aparicio. Quasilinear elliptic problems with singular and homogeneous lower order terms. Nonlinear Anal., 179:105-130, 2019. https://doi.org/10.1016/j.na.2018.08.002