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- Title
Subcritical nonlocal problems with mixed boundary conditions.
- Authors
Molica Bisci, Giovanni; Ortega, Alejandro; Vilasi, Luca
- Abstract
By using linking and ∇ -theorems in this paper we prove the existence of multiple solutions for the following nonlocal problem with mixed Dirichlet–Neumann boundary data, (− Δ) s u = λ u + f (x , u) in Ω , u = 0 on Σ , ∂ u ∂ ν = 0 on Σ , where (− Δ) s , s ∈ (1 / 2 , 1) , is the spectral fractional Laplacian operator, Ω ⊂ ℝ N , N > 2 s , is a smooth bounded domain, λ > 0 is a real parameter, ν is the outward normal to ∂ Ω , Σ , Σ are smooth (N − 1) -dimensional submanifolds of ∂ Ω such that Σ ∪ Σ = ∂ Ω , Σ ∩ Σ = ∅ and Σ ∩ Σ ¯ = Γ is a smooth (N − 2) -dimensional submanifold of ∂ Ω.
- Subjects
NONLINEAR theories; SUBMANIFOLDS; LAPLACIAN operator; DIRICHLET problem; DATA analysis
- Publication
Bulletin of Mathematical Sciences (World Scientific), 2024, Vol 14, Issue 1, p1
- ISSN
1664-3607
- Publication type
Article
- DOI
10.1142/S166436072350011X