Some geometric estimates of the first eigenvalue of quasilinear and (p,q)-Laplace operators


Abstract


In this paper, we use a particular smooth function f:\Omega \rightarrow \mathbb{R} on a bounded domain \Omega of a Riemannian manifold M to estimate the lower bound of the first eigenvalue for quasilinear operator Lf=-\Delta_{p}f+V\vert f\vert^{p-2}f. In this way, we also present a lower bound for the first eigenvalue of the (p,q)-Laplacian on compact manifolds.

DOI Code: 10.1285/i15900932v44n2p45

Keywords: (p,q)-Laplacian; quasilinear operator; first eigenvalue

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