Simplicity and stability of the first eigenvalue of a nonlinear elliptic system.

El Khalil, Abdelouahed; El Manouni, Said; Ouanan, Mohammed

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Displaying similar documents to “Simplicity and stability of the first eigenvalue of a nonlinear elliptic system.”

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The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as R^N. The proof is based on the Picone’s identity which is very useful in problems involving p-Laplacian. In a second part, we study some properties of the first eigenvalue for a system of p-Laplacian. We use Díaz-Saá’s inequality to prove uniqueness and Egorov’s theorem for the isolation. These results generalize J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis...

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In this paper we get the existence results of the nontrivial weak solution (λ,u) of the following eigenvalue problem of quasilinear elliptic systems -D_α (a_αβ(x,u) D_βuⁱ) + 1/2 D_uⁱ a_αβ(x,u)D_αu^j D_βu^j + h(x) uⁱ = ...

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In this paper, we consider shape optimization problems for the principal eigenvalues of second order uniformly elliptic operators in bounded domains of $ℝ^{n}$ . We first recall the classical Rayleigh-Faber-Krahn problem, that is the minimization of the principal eigenvalue of the Dirichlet Laplacian in a domain with fixed Lebesgue measure. We then consider the case of the Laplacian with a bounded drift, that is the operator $- Δ + v \cdot \nabla$ , for which the minimization problem is still well posed. Next, we...