The paper presents the foundations of theory linear fractional Volterra integro-differential equations convolution type in Banach spaces. It is established that existence a resolvent operator for such equivalent to well-posedness formulation initial problem them. Within framework this approach, theorem Hille–Yosida proved.

A class of nonlinear elliptic and parabolic optimal control problems with mixed control-state constraints is considered. Extending a method known for the control of ordinary differential equations to the case of PDEs, the Yosida-Hewitt theorem is applied to show that the Lagrange multipliers are functions of certain Lp-spaces. By bootstrapping arguments, under natural assumptions, optimal contr...

The main purpose of this paper is to prove the existence of the fuzzy core of an exchange economy with a heterogeneous divisible commodity in which preferences of players are concave measures defined on a σ-algebra of admissible pieces of the total endowment of the commodity. The problem is formulated as the partitioning of a measurable space among finitely many players. Applying the Yosida– He...

We show that a locally Lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point. We present a sufficient condition for the semismoothness of solutions to generalized equations over cone reducible (nonpolyhedral) convex sets. We prove that the semismoothness of solutions to the Moreau-Yosida regularization of a lower sem...

In this paper we discuss second-order properties of the Moreau-Yosida regularization F of a piecewise twice continuously differentiable convex function f . We introduce a new constraint qualification in order to prove that the gradient of F is piecewise continuously differentiable. In addition, we discuss conditions, depending on the Hessians of the pieces, that guarantee positive definiteness ...

We present a simplified one-dimensional model for pulse wave propagation through fluid-filled tubes with elastic walls, which takes into account the elasticity of the wall as well as the tapering effect. The spatial dynamics in this model is governed by a variable coefficient KdV equation with conditions given at the inflow site. We discuss an existence theory for the associated evolution equat...

We analyze a potentially risk-averse convex stochastic optimization problem, where the control is deterministic and state Banach-valued essentially bounded random variable. obtain strong forms of necessary sufficient optimality conditions for problems subject to equality conical constraints. propose Moreau-Yosida regularization constraint show consistency regularized problem as parameter taken ...