Properness and Topological Degree for General Elliptic Operators

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

Partially continuous pretopological and topological operators for intuitionistic fuzzy sets

In this paper, pretopological and topological operators are introduced based on partially continuous linear transformations of the membership and non-membership functions for intuitionistic fuzzy sets. They turn out to be a generalization of the topological operators for intuitionistic fuzzy sets.On the other hand it is a generalization of the fuzzy set pretopological operators introduced...

Some properties of continuous linear operators in topological vector PN-spaces

The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

Properness and Topological Degree for Nonlocal Reaction-Diffusion Operators

and Applied Analysis 3 where a± ∂F ∂u ( w±, w± ) , b± ∂F ∂U ( w±, w± ) . 1.9 We will now recall the main definitions and results concerning the essential spectrum and Fredholm property for linear operators and the properness of nonlinear operators. 1.1. Essential Spectrum and Fredholm Property Let us recall that a linear operator M : E1 → E2 acting from a Banach space E1 into another Banach spa...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators