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The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
(Springer Heidelberg, 2016-10)
In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ ...
A limiting problem for local/non-local p-Laplacians with concave–convex nonlinearities
(Birkhauser Verlag Ag, 2020-12)
In this manuscript, we deal with an equation involving a combination of quasi-linear elliptic operators of local and non-local nature with p-structure, and concave?convex nonlinearities. The prototypical model is given by ...
Multiplicity Results for the Fractional Laplacian in Expanding Domains
(2018-06-01)
In this paper, we establish a multiplicity result of nontrivial weak solutions for the problem (- Δ) αu+ u= h(u) in Ω λ, u= 0 on ∂Ω λ, where Ω λ= λΩ , Ω is a smooth and bounded domain in RN, N> 2 α, λ is a positive parameter, ...
On the first nontrivial eigenvalue of the ∞-Laplacian with Neumann boundary conditions
(University of Houston, 2016-06)
We study the limit as p goes to infinity of the first non-zero eigenvalue λp of the p-Laplacian with Neumann boundary conditions in a smooth bounded domain U of Rn. We prove that λ∞:=lim λp1/p=2/diam(U), where diam(U) ...
Bubbling solutions for nonlocal elliptic problems
(European Mathematical Society Publishing House, 2017)
We investigate bubbling solutions for the nonlocal equation Aω s u = up, u > 0 in ω, under homogeneous Dirichlet conditions, where ω is a bounded and smooth domain. The operator As ω stands for two types of nonlocal ...
Multiple solutions for a problem with resonance involving the p-Laplacian
(Abstract and Applied Analysis, 2018)
Multiple Ordered Solutions for a Class of Problems Involving the 1-Laplacian Operator
(2022-04-01)
In this paper, we use minimax methods, comparison arguments, and an approximation result to show the existence and multiplicity of solutions for the following class of problems: {-Δ1v=λf(v)inΩ,v≥0inΩ,v=0on∂Ω,where Ω is a ...
Multiplicity of solutions for a class of quasilinear problems involving the 1-Laplacian operator with critical growth
(2022-01-25)
The aim of this paper is to establish two results about multiplicity of solutions to problems involving the 1-Laplacian operator, with nonlinearities with critical growth. To be more specific, we study the following problem ...
Regularity theory and high order numerical methods for the (1D)-fractional Laplacian
(American Mathematical Society, 2017-03)
This paper presents regularity results and associated high-order numerical methods for one-dimensional Fractional-Laplacian boundary-value problems. On the basis of a factorization of solutions as a product of a certain ...
The spherical p-harmonic eigenvalue problem in non-smooth domains
(Academic Press INC Elsevier Science, 2018)
We prove the existence of p-harmonic functions under the form u(r, sigma) = r(-beta)omega(sigma) in any cone C-S generated by a spherical domain S and vanishing on partial derivative C-S. We prove the uniqueness of the ...