arXiv subjects

Emmanuel Wend-Benedo Zongo

Publications and source records attributed to Emmanuel Wend-Benedo Zongo.

6 recordsLinked to original sources

arXiv2025

Eigenvalues of nonlinear $(p,q)$-fractional Laplace operators under nonlocal Neumann conditions

In this paper, we investigate on a bounded open set of $\mathbb{R}^N$ with smooth boundary, an eigenvalue problem involving the sum of nonlocal operators $(-Δ)_p^{s_1}+ (-Δ)_q^{s_2}$ with $s_1,s_2\in (0,1)$, $p,q\in (1,\infty)$ and subject to the corresponding homogeneous nonlocal $(p,q)$-Neumann boundary condition. A careful analysis of the considered problem leads us to a complete description of the set of eigenvalues as being the precise interval $\{0\}\cup(λ_{1}(s_2,q),\infty)$, where $λ_{1}(s_2,q)$ is the first nonzero eigenvalue of the homogeneous fractional $q$-Laplacian under nonlocal $q$-Neumann boundary condition. Furthermore, we establish that every eigenfunctions is globally bounded.

math.AP↗

arXiv2024

Bifurcation results and multiple solutions for the fractional $(p,q)$-Laplace operators

We investigate a nonlinear nonlocal eigenvalue problem involving the sum of fractional $(p,q)$-Laplace operators $(-Δ)_p^{s_1}+(-Δ)_q^{s_2}$ with $s_1,s_2\in (0,1)$; $p,q\in(1,\infty)$ and subject to Dirichlet boundary conditions in an open bounded set of $\mathbb{R}^N$. We prove bifurcation results from trivial solutions and from infinity for the considered nonlinear nonlocal eigenvalue problem. We also show the existence of multiple solutions of the nonlinear nonlocal problem using variational methods.

math.AP↗

arXiv2023

Null-controllability for a fourth order parabolic equation under general boundary conditions

In this paper, we consider a fourth order inner-controlled parabolic equation on an open bounded subset of $R^d$, or a smooth compact manifold with boundary, along with general boundary operators fulfilling the Lopatinskii-Sapiro condition. We derive a spectral inequality for the solution of the parabolic system that yields a null-controllability result. The spectral inequality is a consequence of an interpolation inequality obtained via a Carleman inequality for the bi-Laplace operator under the considered boundary conditions.

math.AP↗

arXiv2022

Bifurcation results for quasi-linear operators from the Fucik spectrum of the Laplacian

In this paper, we analyze an eigenvalue problem for a quasi-linear elliptic operators involving Dirichlet boundary condition in an open smooth bounded set of $\mathbb{R}^N$. We investigate a bifurcation results (from trivial solution and from infinity) of an eigenvalue problem involving the $(p,2)$-Laplace operator, from the Fu\v cik spectrum of the Laplacian.

math.AP↗

arXiv2022

Bifurcation results for nonlinear eigenvalue problems involving the (p,q)-Laplace operator

In this paper, we analyze an eigenvalue problem for nonlinear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We prove bifurcation results from trivial solutions and from infinity for the considered nonlinear eigenvalue problem. We also show the existence of multiple solutions of the nonlinear problem using variational methods.

math.AP↗

arXiv2021

Stabilization of the damped plate equation under general boundary conditions

We consider a damped plate equation on an open bounded subset of R^d, or a smooth manifold, with boundary, along with general boundary operators fulfilling the Lopatinskii-Sapiro condition. The damping term acts on a region without imposing a geometrical condition. We derive a resolvent estimate for the generator of the damped plate semigroup that yields a logarithmic decay of the energy of the solution to the plate equation. The resolvent estimate is a consequence of a Carleman inequality obtained for the bi-Laplace operator involving a spectral parameter under the considered boundary conditions. The derivation goes first though microlocal estimates, then local estimates, and finally a global estimate.

math.AP↗