Eigenvalues of some nonlinear operators

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

On the Extended Eigenvalues of Some Volterra Operators

Commutator Bounds for Eigenvalues of Some Diierential Operators

Eigenvalues for Radially Symmetric Non-variational Fully Nonlinear Operators

In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear operators exists in the framework of viscosity solutions. Here we want to show that for the radially symmetric operators (and one dimensional) a much simpler the...

Correctors for Some Nonlinear Monotone Operators

In this paper we study homogenization of quasi-linear partial differential equations of the form −div (a (x, x/εh, Duh)) = fh on Ω with Dirichlet boundary conditions. Here the sequence (εh) tends to 0 as h → ∞ and the map a (x, y, ξ) is periodic in y, monotone in ξ and satisfies suitable continuity conditions. We prove that uh → u weakly in W 1,p 0 (Ω) as h → ∞, where u is the solution of a hom...