Keyword: ∇-theorems : Search

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

Advanced Search

SEARCH GUIDE

Results: 1 - 1of1

Follow results:

per page:

Sort: Relevance

Context for search term 1Search term 1*

All Dates

LastSelect static range

Custom Range

Select starting monthSelect starting year

Select ending monthSelect ending year

Search name	Searched On	Run search
Keyword: ∇-theorems (1)	29 Mar 2025	Run
Keyword: Moiré Pattern (2)	29 Mar 2025	Run
Keyword: Data Visualization (30)	29 Mar 2025	Run
Keyword: Center Of Pressure (20)	29 Mar 2025	Run
Keyword: Schwarzschild-like (1)	29 Mar 2025	Run

articleOpen Access
Subcritical nonlocal problems with mixed boundary conditions
Bulletin of Mathematical Sciences10 Aug 2023
Preview Abstract
By using linking and $\nabla$ $\nabla$ -theorems in this paper we prove the existence of multiple solutions for the following nonlocal problem with mixed Dirichlet–Neumann boundary data,
$\{\begin{matrix} {(- Δ)}^{s} u = λ u + f (x, u) & in Ω, \\ u = 0 & on Σ_{𝒟}, \\ \frac{\partial u}{\partial ν} = 0 & on Σ_{𝒩}, \end{matrix}$
where ${(- Δ)}^{s}$ , $s \in (1 / 2, 1)$ , is the spectral fractional Laplacian operator, $Ω \subset ℝ^{N}$ , $N > 2 s$ , is a smooth bounded domain, $λ > 0$ is a real parameter, $ν$ is the outward normal to $\partial Ω$ , $Σ_{𝒟}$ , $Σ_{𝒩}$ are smooth $(N - 1)$ -dimensional submanifolds of $\partial Ω$ such that $Σ_{𝒟} \cup Σ_{𝒩} = \partial Ω$ , $Σ_{𝒟} \cap Σ_{𝒩} = \emptyset$ and $Σ_{𝒟} \cap {\bar{Σ}}_{𝒩} = Γ$ is a smooth $(N - 2)$ -dimensional submanifold of $\partial Ω$ .

1