On singular nonhomogeneous elliptic equations involving critical Caffarelli–Kohn–Nirenberg exponent

Bouchekif, Mohammed; Matallah, Atika

doi:10.1007/s11587-009-0056-y

Cited by 11 publications

(4 citation statements)

References 10 publications

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“…Wang and Zhou [3] have proved that (P 0,μ,1 ), for f(x) ≡ h(x) ≡ 1 and a � 0, has at least two distinct solutions when 0 ≤ μ < μ 0 ≔ ((N − 2)/2) 2 and under some suffcient conditions on f. In [4], Bouchekif and Matallah have shown the existence of two nontrivial solutions of (P a,η,μ )…”

Section: Introductionmentioning

confidence: 99%

Multiple Solutions for Singular Systems with Sign-Changing Weight, Nonlinear Singularities and Critical Exponent

El Mokhtar Ould El Mokhtar,

Aljurbua

2024

International Journal of Differential Equations

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This paper is an attempt to establish the existence and multiplicity results of nontrivial solutions to singular systems with sign-changing weight, nonlinear singularities, and critical exponent. By using variational methods, the Nehari manifold, and under sufficient conditions on the parameter η which represent some physical meanings, we prove some existing results by researching the critical points as the minimizers of the energy functional associated with the proposed problem (2) on the constraint defined by the Nehari manifold, which are solutions of our system, under some sufficient conditions on the parameters α, β, μ, and η. To the best of our knowledge, this paper is one of the first contributions to the study of singular systems with sign-changing weight, nonlinear singularities, and critical exponent.

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Section: Introductionmentioning

confidence: 99%

Multiple Solutions for Singular Systems with Sign-Changing Weight, Nonlinear Singularities and Critical Exponent

El Mokhtar Ould El Mokhtar,

Aljurbua

2024

International Journal of Differential Equations

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“…Wang and Zhou [13] proved that there exist at least two solutions for (1.1) with a = 0, 0 < µ ≤ μ0 = (N − 2) 2 /4. Bouchekif and Matallah [4] showed the existence of two solutions of (1.1) under certain conditions on a weighted function h, when 0 < µ ≤ μa , λ ∈ (0, Λ * ), −∞ < a < (N − 2)/2 and a ≤ b < a + 1, with Λ * a positive constant.…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions for singular elliptic problems with singular nonlinearities and critical Caffarelli-Kohn-Nirenberg exponent

El Mokhtar

2023

ejde

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In this article, we consider a singular elliptic problem with singular nonlinearities and critical Caffarelli-Kohn-Nirenberg exponent. By using variational methods and Palais-Smale condition, we show the existence of at least two nontrivial solutions. The result depends crucially on the parameters \(a,b,N,\beta,\gamma,\lambda,\mu\). For more information see https://ejde.math.txstate.edu/Volumes/2023/54/abstr.html

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“…is well defined among other properties, that is to say, the existence of (at least) two critical points for J λ . Similarly, it was studied in [5] the existence of nontrivial solutions for the following problem…”

Section: Introductionmentioning

confidence: 99%

A scaling approach to Caffarelli-Kohn-Nirenberg inequality

Bazan,

Neves

2013

Preprint

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We consider the general Caffarelli-Kohn-Nirenberg inequality in the Euclidean and Remannian setting. From a new parameter introduced, the proof of the former case, follows by simple interpolation arguments and Hölder's inequality. Moreover, the ranges of this convenient parameter completely characterize the inequality. Secondly, the same technics are used to study the Caffarelli-Kohn-Nirenberg inequality in the Riemannian case.

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On singular nonhomogeneous elliptic equations involving critical Caffarelli–Kohn–Nirenberg exponent

Abstract: In this paper, we establish the existence of multiple solutions for nonhogeneous singular elliptic equations involving critical Caffarelli-Kohn-Nirenberg exponent, by using Ekeland's Variational Principle and Mountain Pass Theorem without Palais Smale conditions.

Cited by 11 publications

References 10 publications

Multiple Solutions for Singular Systems with Sign-Changing Weight, Nonlinear Singularities and Critical Exponent

Multiple Solutions for Singular Systems with Sign-Changing Weight, Nonlinear Singularities and Critical Exponent

Existence of solutions for singular elliptic problems with singular nonlinearities and critical Caffarelli-Kohn-Nirenberg exponent

A scaling approach to Caffarelli-Kohn-Nirenberg inequality

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