Webwhich means that u is an eigenfunction of (6.1) with corresponding eigenvalue m. It only remains to show that m is the smallest eigenvalue. Suppose v is another eigen-function … Web14 de mai. de 2014 · We show among other things that the limit of the eigenvalue, at least for convex sets, is in fact the first nonzero eigenvalue of the limiting problem. We then derive a number of consequences, which are nonlinear analogues of well-known inequalities for the linear (2-)Laplacian.
Eigenvalue problems for the p-Laplacian with indefinite weights
Web1 de fev. de 2024 · In recent paper [6], Hua and Wang studied eigenvalues and eigenfunctions of p-Laplacians with Dirichlet boundary condition on graphs and identified … WebThe goal of this paper is to prove new upper bounds for the first positive eigenvalue of the p-Laplacian operator in terms of the mean curvature and constant sectional curvature on Riemannian manifolds.In particular, we provide various estimates of the first eigenvalue of the p-Laplacian operator on closed orientate n-dimensional Lagrangian submanifolds in … fluff article
The second eigenvalue of the fractional $p-$Laplacian
Web14 de abr. de 2024 · We consider the spectral problem for the mixed local and nonlocal p-Laplace operator. We discuss the existence and regularity of eigenfunction of the associated Dirichlet (p, q)-eigenvalue problem in a bounded domain Ω ⊂ ℝ N under the assumption that 1 < p < ∞ and 1 < q < p ∗ where p ∗ = Np/ (N − p) if 1 < p < N and p ∗ = ∞ if ... Web1 de mar. de 2013 · Abstract. The second largest Laplacian eigenvalue of a graph is the second largest eigenvalue of the associated Laplacian matrix. In this paper, we study extremal graphs for the extremal values of the second largest Laplacian eigenvalue and the Laplacian separator of a connected graph, respectively. All simple connected graphs … Web1 de out. de 2016 · Abstract. We consider the eigenvalue problem for the fractional p-Laplacian in an open bounded, possibly disconnected set Ω ⊂ ℝ n, under homogeneous … greene county georgia republican party