u ′t + Aut = ft, t ∈ 0,T u0 = u0, where Au,vH = Bu,v ∀u,v ∈ V ⊂ H ⊂ V ′. We showed that if the bilinear form B is coercive then the linear mapping A is an isomorphism from V onto V’. Recall that there exists a family of H-orthonormal eigenfunctions for A such that ||Awk ||H = |λk| ||wk ||H = |λk|→ ∞ as k → ∞. Then A is clearly not bounded as a mapping from H into H. If we define D...

Stationary Problem I We consider a mapping, A : X 7→ Y , given explicitly by A(u) = Lu+ a(u, u, · ) + F (u, · ), where L : X 7→ X is an isomorphism. The structure of L is induced by a continuous, coercive bilinear form B(· , · ) on X ⊗X: 〈Lu, v〉 = B(u, v), B(u, u) ≥ c‖u‖. Charge Transport in anIncompressible Fluid Medium – p. 31/63 Abstract Stationary Problem I We consider a mapping, A : X 7→ Y...

and Applied Analysis 3 The generalized mixed equilibrium problems with perturbation is very general in the sense that it includes fixed point problems, optimization problems, variational inequality problems, Nash equilibrium problems, and equilibrium problems as special cases see, e.g., 4, 5 . Numerous problems in physics, optimization, and economics reduce to find a solution of problem 1.2 . S...

A graph G = (V,E) is a threshold graph if there is a mapping a : V → R+ and a positive real number S such that a(v) < S for all v ∈ V and (v, w) ∈ E if and only if a(v) + a(w) ≥ S. It is well known that G can be partitioned into a clique K and a stable set I. Threshold graphs constitute a very important and well studied class in graph theory and graph algorithms, since they have applications in...

and Applied Analysis 3 where A n = α n I + A for all n ≥ 0. In particular, if V ≡ 0, then (11) reduces to the following iterative scheme: x 0 = x ∈ C chosen arbitrarily, y n = P C (x n − ] n A n x n ) , z n = β n x n + γ n P C (x n − ] n A n y n ) + σ n TP C (x n − ] n A n y n ) , x n+1 = P C [λ n (1 − δ n ) γSx n + (I − λ n μF) z n ] , ∀n ≥ 0. (12) Further, if S = V, then (11) reduces to the f...