A quasilinear singular elliptic system without cooperative structure

Motreanu, Dumitru; Moussaoui, Abdelkrim

doi:10.1016/s0252-9602(14)60058-8

Cited by 30 publications

(22 citation statements)

References 12 publications

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“…However, it is worth notting that the obtained sub-and supersolution are quite different from the functions considered in the quoted papers, especially those constructed in [2,3]. Practically and contrary to preconceived ideas, the construction process of the sub-and super-solutions in the present work is broadly similar to the one used in the case of constant exponent problems (see, e.g., [7,18,19]), despite the loss of the homogeneity property of the operator ∆ p i (x) , which constitutes in itself a major obstacle to face. The crucial aspect of the argument is the new Mean Value Theorem (cf.…”

Section: Introductionmentioning

confidence: 71%

“…The authors obtained the existence of solutions through new theorems involving sub and supersolutions for singular systems with variable exponents by dealing with cooperative and competitive structures. However, when the exponent variable functions p(·), q(·), α i (·) and β i (·), i = 1, 2, are reduced to be constants, problem (P ) have been thoroughly investigated, we refer to [19] for system (P ) with cooperative structure, while we quote [17,18] for the study of competitive structure in (P ). Furthermore, in the constant exponent context, the singular problem (P ) arise in several physical situations such as fluid mechanics, pseudoplastics flow, chemical heterogeneous catalysts, non-Newtonian fluids, biological pattern formation, for more details about this subject, we cite the papers of Fulks & Maybe [12], Callegari & Nashman [7,8] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Existence and a priori estimates of solutions for quasilinear singular elliptic systems with variable exponents

Moussaoui

Vélin

2018

J Elliptic Parabol Equ

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This article sets forth results on the existence, a priori estimates and boundedness of positive solutions of a singular quasilinear systems of elliptic equations involving variable exponents. The approach is based on Schauder's fixed point Theorem. A Moser iteration procedure is also obtained for singular cooperative systems involving variable exponents establishing a priori estimates and boundedness of solutions. C1

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Section: Introductionmentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Existence and a priori estimates of solutions for quasilinear singular elliptic systems with variable exponents

Moussaoui

Vélin

2018

J Elliptic Parabol Equ

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“…The sublinear condition α 2 < q − 1 and β 1 < p − 1 for singular systems of type (1.1) have been thoroughly investigated. For a complete overview on the study of the infinite positone problem (1.1) we refer to [1,2,15,17], while for the study of the infinite semipositone problem (1.1), we cite [5,13,14]. We also mention [6,7] focusing on the semilinear case of (1.1), that is, when p = q = 2.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Positive solutions for infinite semipositone/positone quasilinear elliptic systems with singular and superlinear terms

Khodja¹,

Moussaoui²

2016

Differential Equations &Amp; Applications

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“…Problem (P ) ± without a convection term, that is g = 0 was also investigated. [24]. From the above commentaries, we observe that in recent years singular elliptic problems with convection term has received few attention.…”

Section: Introductionmentioning

confidence: 97%

Existence of solutions for a class of singular elliptic systems with convection term

Alves

Moussaoui

2014

Asymptotic Analysis

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We show the existence of positive solutions for a class of singular elliptic systems with convection term. The approach combines sub-and supersolution method with the pseudomonotone operator theory and perturbation arguments involving singular terms. Systems (S) ± can be see as a version of the singular scalar equations± with α, β > 0 and g : R N → R be a continuous function verifying some technical conditions. Several works are devoted to classes of problems covering (P ) ± . For instance, see the papers of Aranda [5], Ghergu and Radulescu [19,20], Giarrusso and Porru [21], Lair and Wood [24], Zhang [29] and references therein. Problem (P ) ± without a convection term, that is g = 0 was also investigated. Relevant contributions regarding this situation can be found in [8-12,14]. The main tools used in the aforementioned works are Sub-and Supersolution, Fixed Point Theorems, Bifurcation Theory and Galerkin Method. On the other hand, using variational technique, more precisely mountains pass theorem, de Figueiredo, Girardi and Matzeu [13] studied a class of elliptic problems without singularity, where the nonlinearity depends of the gradient of the solution. Related to systems (S) ± , to date, the only case considered in the literature, known to authors for g i = 0 is the paper due to Alves, Carrião and Faria [1]. For the case where g i = 0, we refer the reader to the survey paper by Alves and Corrêa [2], Alves, Corrêa and Gonçalves [3], El Manouni, Perera and Shivaji [15], Ghergu [17,18], Hernández, Mancebo and Vega [22], Montenegro and Suarez [26] and Motreanu and Moussaoui [27]. From the above commentaries, we observe that in recent years singular elliptic problems with convection term has received few attention. Motivated by this fact, our aim is to show the existence of solutions for a class of elliptic systems where the nonlinearity besides a singular term has a convection term. The proof combines results involving pseudomonotone operators, sub-and supersolution method and perturbation arguments involving singular terms. We emphasize that our study complete those made in [2,3] and [27], in the sense that in those papers the authors did not consider the case where the nonlinearity has a convection term, and also [1], because a different type of singular term was considered. The method used in the present work is different from those applied in the aforementioned papers.Our main result is the following theorem.

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A quasilinear singular elliptic system without cooperative structure

Cited by 30 publications

References 12 publications

Existence and a priori estimates of solutions for quasilinear singular elliptic systems with variable exponents

Existence and a priori estimates of solutions for quasilinear singular elliptic systems with variable exponents

Positive solutions for infinite semipositone/positone quasilinear elliptic systems with singular and superlinear terms

Existence of solutions for a class of singular elliptic systems with convection term

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