We consider a second order three point boundary value problem for dynamic equations on time scales and establish criteria for the existence of at least two positive solutions of an eigenvalue problem by an application of a fixed point theorem in cones. Existence result for non-eigenvalue problem is also given by the monotone method.

In this paper we study an eigenvalue boundary value problem which arises when seeking radial convex solutions of the Monge-Ampère equations. We shall establish several criteria for the existence, multiplicity and nonexistence of strictly convex solutions for the boundary value problem with or without an eigenvalue parameter.

The main ideas of path following by predictor-corrector and piecewise-linear methods, and their application in the direction of homotopy methods and non-linear eigenvalue problems are reviewed. Further new applications to areas such as polynomial systems of equations, linear eigenvalue problems, interior methods for linear programming, parametric programming and complex bifurcation are surveyed...

We propose an efficient eigensolver for computing densely distributed spectrum of the two-dimensional transmission eigenvalue problem (TEP) which is derived from Maxwell’s equations with Tellegen media and the transverse magnetic mode. The discretized governing equations by the standard piecewise linear finite element method give rise to a large-scale quadratic eigenvalue problem (QEP). Our num...

By considering the three-dimensional incompressible Euler equations, a 4-vector ζ is constructed out of a combination of scalar and vector products of the vorticity ω and the vortex stretching vector ω · ∇u = Sω. The evolution equation for ζ can then be cast naturally into a quaternionic Riccati equation. This is easily transformed into a quaternionic zero-eigenvalue Schrödinger equation whose ...