Abstract We study the optimal arrangement of two conductive materials in order to maximize first eigenvalue corresponding diffusion operator with Dirichlet conditions. The amount highest composite is assumed be limited. Since this type problems has no solution general, we work a relaxed formulation. show that problem some good concavity properties which allow us get uniqueness results. By provi...

We give lower and upper bounds for the first eigenvalue of geodesic balls in spherically symmetric manifolds. These lower and upper bounds are C0-dependent on the metric coefficients. It gives better lower bounds for the first eigenvalue of spherical caps than those from Betz-Camera-Gzyl. Mathematics Subject Classification: (2000):35P15, 58C40.

in this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularitiesin a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g.freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular pointsand turning points, math. nachr...

We estimate the lower bound of the first Dirichlet eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature in terms of the diameter and the lower bound of Ricci curvature and give an affirmative answer to the conjecture of H. C. Yang for the first Dirichlet eigenvalue.

We prove that every eigenvalue of a Robin problem with boundary parameter α on a sufficiently smooth domain behaves asymptotically like −α as α → ∞. This generalises an existing result for the first eigenvalue.