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].

is completely integrable and hence L(k) is in a commuting system of differential operators with n algebraically independent operators. Then we have the following fundamental result (cf. [1]). Theorem [Heckman, Opdam]. When kα are generic, the function F (λ, k;x) has an analytic extension on R and defines a unique simultaneous eigenfunction of the commuting system of differential operators with ...

We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case that we consider here, our methods require only C3 regularity of the maps in the IFS. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linea...

The solution for a simply supported many-sided polygonal plate does not agree with that for the corresponding circular plate. This paper describes the earlier work of Rao and Rajaiah on polygonal plates and then explains why best convergence of series solutions occurs when the boundary conditions are denned as w = Vw> = 0. Notation D — operator in original problems, D = operator adjoint to D, F...

Nonlinear variational methods have become very powerful tools for many image processing tasks. Recently a new line of research has emerged, dealing with nonlinear eigenfunctions induced by convex functionals. This has provided new insights and better theoretical understanding of convex regularization and introduced new processing methods. However, the theory of nonlinear eigenvalue problems is ...

This paper proposes a novel adaptive higher-order finite element (hp-FEM) method for solving elliptic eigenvalue problems, where n eigenpairs are calculated simultaneously, but on individual meshes. The meshes automatically hp-refined independently of each other, with the goal to use an optimal mesh sequence eigenfunction. and algorithm described in detail. Numerical examples clearly demonstrat...

We consider general linear non-degenerate weak-coupled cooperative elliptic systems and study certain monotonicity properties of the generalized principal eigenvalue in Rd with respect to potential. It is shown that on right equivalent recurrence property twisted operator which is, turn, minimal growth at infinity eigenfunctions. The strict be exponential stability operators. An equivalence bet...

We consider a general second order uniformly elliptic diierential operator L and also the set of all open sets (not neccessarily smooth) in the unit ball of I R n. We deene a metric d in this set (up to an equivalence relation) that makes the space ((= ; d) a complete metric space. We show that the principal eigenvalue and eigenfunction of L are continuous with the metric d. Similar results are...