Positive solutions for a class of non-cooperative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>p</mml:mi><mml:mi>q</mml:mi></mml:math>-Laplacian systems with singularities

Chu, K. D.; Hai, D. D.; Shivaji, R.

doi:10.1016/j.aml.2018.05.024

Cited by 6 publications

(4 citation statements)

References 7 publications

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“…The required compactness of involved operators is ensured by a Hölder regularity result of independent interest they proved for weak energy solutions to a scalar problem associated to () (see also Singh 24 for related issues). Recently, Candito et al 25 and Chu et al 26 used the same approach to get the existence of positive solutions to other kinds of quasilinear elliptic and singular systems (see also previous studies 27–29 for further extensions).…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Nonlinear fractional and singular systems: Nonexistence, existence, uniqueness, and Hölder regularity

Gouasmia

2022

Math Methods in App Sciences

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where Ω ⊂ R N is an open-bounded domain with smooth boundary, s 1 , s 2 ∈ (0, 1), p 1 , p 2 ∈ (1, + ∞), and 𝛼 1 , 𝛼 2 , 𝛽 1 , 𝛽 2 are positive constants. We first discuss the nonexistence of positive classical solutions to system (S). Next, constructing suitable ordered pairs of subsolutions and supersolutions, we apply Schauder's fixed-point theorem in the associated conical shell and get the existence of a positive weak solutions pair to (S), turn to be Hölder continuous. Finally, we apply a well-known Krasnosel'skiı's argument to establish the uniqueness of such positive pair of solutions.

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Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Nonlinear fractional and singular systems: Nonexistence, existence, uniqueness, and Hölder regularity

Gouasmia

2022

Math Methods in App Sciences

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“…Later on, a class of (p, q)-Laplacian system with indefinite weights have been learned by Afrouzi et al in [1] via local minimization techniques. For interested readers, we point out some striking articles [10,13,16,18,19] which deals with various kind of elliptic systems involving the (p, q)-Laplace operator. In [10], the authors have analyzed the existence of positive solutions to the non-cooperative fractional elliptic system and the scheme heavily relies upon the Schauder fixed point theorem.…”

Section: Introductionmentioning

confidence: 99%

“…For interested readers, we point out some striking articles [10,13,16,18,19] which deals with various kind of elliptic systems involving the (p, q)-Laplace operator. In [10], the authors have analyzed the existence of positive solutions to the non-cooperative fractional elliptic system and the scheme heavily relies upon the Schauder fixed point theorem. Using the mechanism of sub-super solutions, the authors in [13] have achieved captivating results about the existence of a weak solution.…”

Section: Introductionmentioning

confidence: 99%

Non-homogeneous $(p_1,p_2)$-fractional Laplacian systems with lack of compactness

Mukherjee,

Mukherjee

2021

Preprint

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The present paper studies the existence of weak solutions for following type of non-homogeneous system of equations (S)where Ω ⊂ R N is smooth bounded domain, s1, s2 ∈ (0, 1), 1 < p1, p2 < ∞, N > max{p1s1, p2s2}, α > −1 and β > −1. We employ the variational techniques where the associated energy functional is minimized over Nehari manifold set while imposing appropriate bound on dual norms of f1, f2.

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“…Many authors have been interested by the problem (1) in different ways [1][2][3][4]. The subsuper solution method, given in [5] by using a monotony argument, is the principal tool used to prove the existence of solution of the problem (1) in [1,3,4].…”

Section: Introductionmentioning

confidence: 99%

Positive solution for the (p, q)-Laplacian systems by a new version of sub-super solution method

Moussa

Mazan

2021

AJMS

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PurposeIn this paper, the authors give a new version of the sub-super solution method and prove the existence of positive solution for a (p, q)-Laplacian system under weak assumptions than usually made in such systems. In particular, nonlinearities need not be monotone or positive.Design/methodology/approachThe authors prove that the sub-super solution method can be proved by the Shcauder fixed-point theorem and use the method to prove the existence of a positive solution in elliptic systems, which appear in some problems of population dynamics.FindingsThe results complement and generalize some results already published for similar problems.Originality/valueThe result is completely new and does not appear elsewhere and will be a reference for this line of research.

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Positive solutions for a class of non-cooperative pq-Laplacian systems with singularities

Cited by 6 publications

References 7 publications

Nonlinear fractional and singular systems: Nonexistence, existence, uniqueness, and Hölder regularity

Nonlinear fractional and singular systems: Nonexistence, existence, uniqueness, and Hölder regularity

Non-homogeneous $(p_1,p_2)$-fractional Laplacian systems with lack of compactness

Positive solution for the (p, q)-Laplacian systems by a new version of sub-super solution method

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