In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction. Dedicated to Prof. Dr. Karel Rektorys on the occasion of his 80th birthday

Certain fully nonlinear elliptic Partial Differential Equations can be written as functions of the eigenvalues of the Hessian. These include: the Monge-Ampère equation, Pucci’s Maximal and Minimal equations, and the equation for the convex envelope. In this article we build convergent monotone finite difference schemes for the aforementioned equations. Numerical results are presented.

The alignment algorithm of Zhang and Zha is an effective method recently proposed for nonlinear manifold learning (or dimensionality reduction). By first computing local coordinates of a data set, it constructs an alignment matrix from which a global coordinate is obtained from its null space. In practice, the local coordinates can only be constructed approximately and so is the alignment matri...

The eigenvalues of the monodromy matrix, known as Floquet characteristic multipliers, are used to study the local stability of periodic motions of a nonlinear system of differential-algebraic equations (DAE). When the size of the underlying system is large, the cost of computing the monodromy matrix and its eigenvalues may be too high. In addition, for non-minimal set equations, such as those o...

Using both the fermionic-like and the bosonic-like properties of the Pauli spin operators we discuss the Bose description of the Pauli spin operators firstly proposed by Shigefumi Naka, and derive another new bosonic representation of Pauli operators. The eigenvector of σ− in the bosonic representation is a nonlinear coherent state with the eigenvalues being the Grassmann numbers.

We find the exact solution of a recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation at N = ∞ for arbitrary dimension D. The nonlinear integral equation for the gauge invariant density of eigenvalues of the vacuum average of the scalar field is derived. In the continuum limit, the density grows as φ α where α = 1 +

We consider the nonlinear eigenvalue problem − div(|∇u|∇u) = λg(x)|u|u in R with p > 1. A condition on indefinite weight function g is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in W (R ). A nonexistence result is also given for the case p ≥ N .

In this paper the Adomian decomposition method is applied to the nonlinear SturmLiouville problem −y + y(t) = λy(t), y(t) > 0, t ∈ I = (0, 1), y(0) = y(1) = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.