On Dirichlet problem for fractional p-Laplacian with singular non-linearity

By T. Mukherjee, Konijeti Sreenadh. 2016

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Abstract In this article, we study the following fractional p-Laplacian equation with critical growth and singular non-linearity: ( - Δ p ) s ⁢ u = λ ⁢ u - q + u α , u > 0 in ⁢ Ω , u = 0 in ⁢ ℝ n ∖ Ω , (-\Delta_{p})^{s}u=\lambda u^{-q}+u^{\alpha},\quad u>0\quad\text{in }\Omega,% \qquad u=0\quad\text{in }\mathbb{R}^{n}\setminus\Omega, where Ω is a bounded domain in ℝ n {\mathbb{R}^{n}} with smooth boundary ∂ ⁡ Ω {\partial\Omega} , n > s ⁢ p {n>sp} , s ∈ ( 0 , 1 ) {s\in(0,1)} , λ > 0 {\lambda>0} , 0 < q ≤ 1 {0<q\leq 1} and 1 < p < α + 1 ≤ p s * {1<p<\alpha+1\leq p^{*}_{s}} . We use variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/84768784e5a681e5fce9e77a8efe627f76e2c312

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On double phase Kirchhoff problems with singular nonlinearity (2021, methodology): “This method has become a very powerful tool and has been used, for example, in the works of Chen-Kuo-Wu [9] (for degenerate Kirchhoff Laplacian problems with sign-changing weight), Fiscella-Mishra [22] (for fractional Kirchhoff problems), Kumar-Rădulescu-Sreenadh [32] (for critical (p, q)-equations)”
Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems (2021, methodology): “The perturbed singular case is investigated by Barrios-De Bonis-Medina-Peral [10], Adimurthi-Giacomoni-Santra [1] for p = 2; MukherjeeSreenadh [57] in the quasilinear case and the references therein.”