5 research outputs found
Bounds for the largest p-Laplacian eigenvalue for graphs
No full textAbstractThis paper is concerned with techniques for quantitative analysis of the largest p-Laplacian eigenvalue. We present some bounds on the largest eigenvalue, which generalize those given in the linear case. Some examples of applications are given. Then, we compare our bounds to the classical bounds in the particular case of the trees
On the Borel-Cantelli Lemma and moments
No full textsummary:We present some extensions of the Borel-Cantelli Lemma in terms of moments. Our result can be viewed as a new improvement to the Borel-Cantelli Lemma. Our proofs are based on the expansion of moments of some partial sums by using Stirling numbers. We also give a comment concerning the results of Petrov V.V., {\it A generalization of the Borel-Cantelli Lemma\/}, Statist. Probab. Lett. {\bf 67} (2004), no. 3, 233--239
On the discrete version of Picone's identity
No full textAbstractFor a real number p with 1<p we consider the first eigenvalues of the p-Laplacian on graphs, and estimates for the solutions of p-Laplace equations on graphs. We provide a discrete version of Picone's identity and its application. More precisely, we prove a Barta-type inequality for graphs with boundary. Finally, we provide a discrete version of the anti-maximum principle
