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pro vyhledávání: '"Nirjan Biswas"'
Autor:
Nirjan Biswas
Publikováno v:
Opuscula Mathematica, Vol 44, Iss 4, Pp 445-470 (2024)
Let \(s\in (0,1)\) and \(N\gt 2s\). In this paper, we consider the following class of nonlocal semipositone problems: \[(-\Delta)^s u= g(x)f_a(u)\text{ in }\mathbb{R}^N,\quad u \gt 0\text{ in }\mathbb{R}^N,\] where the weight \(g \in L^1(\mathbb{R}^N
Externí odkaz:
https://doaj.org/article/c3944c2e91a24fa7b7aa6f37bef932d5
Publikováno v:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics. :1-28
For $N\geq 2$, a bounded smooth domain $\Omega$ in $\mathbb{R}^N$, and $g_0, V_0 \in L^1_{loc}(\Omega)$, we study the optimization of the first eigenvalue for the following weighted eigenvalue problem: \begin{align*} -\Delta_p \phi + V |\phi|^{p-2}\p
Autor:
T. V. Anoop, Nirjan Biswas
For p ∈ ( 1 , ∞ ) , we consider the following weighted Neumann eigenvalue problem on B 1 c , the exterior of the closed unit ball in R N : (0.1) − Δ p ϕ = λ g | ϕ | p − 2 ϕ in B 1 c , ∂ ϕ ∂ ν = 0 on ∂ B 1 , where Δ p is the p -L
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dbb1a18ec74fe07a8ae07cd4c6d30dea
http://arxiv.org/abs/1812.10677
http://arxiv.org/abs/1812.10677
Publikováno v:
Communications on Pure & Applied Analysis. 20:3259
Let $k,N \in \mathbb{N}$ with $1\le k\le N$ and let $\Omega=\Omega_1 \times \Omega_2$ be an open set in $\mathbb{R}^k \times \mathbb{R}^{N-k}$. For $p\in (1,\infty)$ and $q \in (0,\infty),$ we consider the following Hardy-Sobolev type inequality: \be