On differential operators with integral conditions.
On differentiation of metric projections in finite dimensional Banach spaces
On discontinuous implicit differential equations in ordered Banach spaces with discontinuous implicit boundary conditions
We consider the existence of extremal solutions to second order discontinuous implicit ordinary differential equations with discontinuous implicit boundary conditions in ordered Banach spaces. We also study the dependence of these solutions on the data, and cases when the extremal solutions are obtained as limits of successive approximations. Examples are given to demonstrate the applicability of the method developed in this paper.
On discontinuous quasi-variational inequalities
In this paper, we derive a general theorem concerning the quasi-variational inequality problem: find x̅ ∈ C and y̅ ∈ T(x̅) such that x̅ ∈ S(x̅) and ⟨y̅,z-x̅⟩ ≥ 0, ∀ z ∈ S(x̅), where C,D are two closed convex subsets of a normed linear space X with dual X*, and and are multifunctions. In fact, we extend the above to an existence result proposed by Ricceri [12] for the case where the multifunction T is required only to satisfy some general assumption without any continuity. Under a kind of Karmardian’s...
On discreteness of spectrum of a functional differential operator
We study conditions of discreteness of spectrum of the functional-differential operator on . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.
On Diviccaro, Fisher and Sessa open questions
Let be a closed convex subset of a complete convex metric space and two compatible mappings satisfying following contraction definition: for all in , where and . If is continuous and contains , then and have a unique common fixed point in and at this point is continuous. This result gives affirmative answers to open questions set forth by Diviccaro, Fisher and Sessa in connection with necessarity of hypotheses of linearity and non-expansivity of in their Theorem [3]...
On Dominant Operators.
On Dominating Sequences in the Unit Disc.
On duality in spaces of solutions to elliptic systems.
On dyadic spaces and almost Milyutin spaces
On E. Borel's Theorem.
On Edmunds-Triebel spaces.
On Eigenfunction Branches of Nonlinear Operators, and their Bifurcations.
On eigenfunction expansions and scattering theory.
On equilibrium bifurcations in the cosymmetry collapse of a dynamical system.
On equilibrium point in topological vector spaces
On equilibrium problems.
On equivalence of some iterations convergence for quasi-contraction maps in convex metric spaces.
On Erb's uncertainty principle
We improve a result of Erb, concerning an uncertainty principle for orthogonal polynomials. The proof uses numerical range and a decomposition of some multiplication operators as a difference of orthogonal projections.
On ergodic properties of convolution operators associated with compact quantum groups
Recent results of M. Junge and Q. Xu on the ergodic properties of the averages of kernels in noncommutative -spaces are applied to the analysis of almost uniform convergence of operators induced by convolutions on compact quantum groups.