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Zeddini, Noureddine

doi:10.1023/a:1020559619108

Cited by 15 publications

(1 citation statement)

References 9 publications

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“…Here G(x, y) denotes the Green's function of the Laplacian in Ω and the class K(Ω) is defined by [19,28]). The class K(Ω) is quite rich, it contains for example L p (Ω), for p ∈ (1, ∞] and any function of the form (δ(x)) −λ for λ < 2.…”

Section: Introductionmentioning

confidence: 99%

Singular solutions of a nonlinear equation in a punctured domain of <inline-formula><tex-math id="M1">\begin{document}$\mathbb{R}^{2}$\end{document}</tex-math></inline-formula>

Bachar¹,

Mâagli²

2019

Discrete &Amp; Continuous Dynamical Systems - S

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We consider the following singular semilinear problemwhere σ < 1, Ω is a bounded regular domain in R 2 with 0 ∈ Ω. The weight function a(x) is required to be positive and continuous in Ω\{0} with the possibility to be singular at x = 0 and/or at the boundary ∂Ω. When the function a satisfies sharp estimates related to Karamata class, we prove the existence and global asymptotic behavior of a positive continuous solution on Ω\{0} which could blow-up at 0.

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Section: Introductionmentioning

confidence: 99%

Singular solutions of a nonlinear equation in a punctured domain of <inline-formula><tex-math id="M1">\begin{document}$\mathbb{R}^{2}$\end{document}</tex-math></inline-formula>

Bachar¹,

Mâagli²

2019

Discrete &Amp; Continuous Dynamical Systems - S

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On the subordinate killed B.M in bounded domains and existence results for nonlinear fractional Dirichlet problems

2011

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We take up in this paper the existence of positive continuous solutions for some nonlinear boundary value problems with fractional differential equation based on the fractional Laplacian (− |D ) α 2 associated to the subordinate killed Brownian motion process Z D α in a bounded C 1,1 domain D. Our arguments are based on potential theory tools on Z D α and properties of an appropriate Kato class of functions K α (D).

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