We prove that there are only finitely many closed hyperbolic 3-manifolds with injectivity radius and first eigenvalue of the Laplacian bounded below whose fundamental groups can be generated by a given number of elements.

In this work we prove a Lyapunov type inequality for monotone quasilinear operators generalizing the p−Laplacian. This inequality enable us to obtain lower bounds for the first eigenvalue obtained in the setting of Orlicz-Sobolev spaces.

In this work we extend an inequality of Nehari to the eigenvalues of weighted quasilinear problems involving the p-laplacian when the weight is a monotonic function. We apply it to different eigenvalue problems.

In this article, we study a class of boundary value problems with p-Laplacian. By using a “Green-like” functional and applying the fixed point index theory, we obtain eigenvalue criteria for the existence of positive solutions. Several explicit conditions are derived as consequences, and further results are established for the multiplicity and nonexistence of positive solutions. Extensions are ...

On closed Riemannian manifolds with Bakry-Émery Ricci curvature bounded from below and gradient of the potential function, we obtain lower bounds for all positive eigenvalues Beltrami-Laplacian instead weighted Laplacian. The bound k th eigenvalue depends on k, curvature, dimension diameter upper manifold, but volume manifold is not involved.

Abstract We compute the leading coefficient in asymptotic expansion of eigenvalue counting function for Kohn Laplacian on spheres. express as an infinite sum and integral.