An eigenvalue problem on a bounded domain for the Laplacian with a nonlinear Robin-like boundary condition is investigated. We prove the existence, isolation and simplicity of the first two eigenvalues. 2000 Mathematics Subject Classification: 35P30, 35D05, 35J60, 35J70, 58E05.

In this paper we study a nonlinear boundary eigenvalue problema governed by the one-dimensional p-Laplacian operator with impulse, give some properties of first λ1 and prove existence eigenvalues sequence {λn}n∈N∗ using Lusternik-Schnirelman principle, as well characterization eigenvalues, discuss strict monotonicity that eigenfunction corresponding to second λ2 changes sign only once on [0, 1].

We determine intervals for two eigenvalues for which there exists no positive solution of a system of nonlinear differential equations subject to multi-point boundary value problems on time scales. AMS subject classifications: 39A10, 34B15, 34A40

We consider convex solutions of nonlinear elliptic equations which satisfy the structure condition Bian and Guan. prove a weak Harnack inequality for eigenvalues Hessian these s...

We consider the persistence and stability of dark solitons in the Gross–Pitaevskii (GP) equation with a small decaying potential. We show that families of black solitons with zero speed originate from extremal points of an appropriately defined effective potential and persist for sufficiently small strength of the potential. We prove that families at the maximum points are generally unstable wi...

Eigenvectors and eigenvalues of discrete graph Laplacians are often used for manifold learning and nonlinear dimensionality reduction. It was previously proved by Belkin and Niyogi [3] that the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator of the manifold in the limit of infinitely many data points sampled ind...

Under rotation-equivariant decision theory, sample covariance matrix eigenvalues can be optimally shrunk by recombining eigenvectors with a (potentially nonlinear) function of the unobservable population matrix. The optimal shape this reflects loss/risk that is to minimized. We solve problem estimation under variety loss functions motivated statistical precedent, probability and differential ge...

We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form T (λ)v = 0 that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are generalizations of linear Hermitian eigenproblems Av=λBv. In this paper, we propose a Preconditioned Locally Minimal Residual (PLMR) method for efficiently computing interior...