Spectrum of a Class of Difference Operators with Indefinite Weights

On the Fučik Spectrum with Indefinite Weights

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 Positive Solution for a Class of Nonlinear Elliptic Systems with Indefinite Weights

We establish the existence of a nontrivial solution of system:  −∆pu = λ a(x)u|u|p−2 + λ′c(x)u|u|α−1|v|β+1 + f in Ω −∆qv = μ b(x)v|v|q−2 + λ′c(x)|u|α+1v|v|β−1 + g in Ω (u, v) ∈W 1,p 0 (Ω)×W 1,q 0 (Ω) under some restrictions on λ, μ, λ′, α, β, f and g. We show this result by a local minimization.

Existence Result for a Class of Elliptic Systems with Indefinite Weights in R2

Asymmetric Elliptic Problems with Indefinite Weights

– We prove the existence of a first nontrivial eigenvalue for an asymmetric elliptic problem with weights involving the laplacian (cf. (1.2) below) or more generally the p-laplacian (cf. (1.3) below). A first application is given to the description of the beginning of the Fučik spectrum with weights for these operators. Another application concerns the study of nonresonance for the problems (1....