Lipschitz integral operators represented by vector measures

<p>In this paper we introduce the concept of Lipschitz Pietsch-p-integral <br />mappings, (1≤p≤∞), between a metric space and a Banach space. We represent these mappings by an integral with respect to a vector<br />measure defined on a suitable compact Hausdorff space, obtaining in this way a rich factorization theory through the classical Banach spaces C(K), L_p(μ,K) and L_∞(μ,K). Also we show that this type of operators fits in the theory of composition Banach Lipschitz operator ideals. For p=∞, we characterize the Lipschitz Pietsch-∞-integral mappings by a factorization schema through a weakly compact operator. Finally, the relationship between these mappings and some well known Lipschitz operators is given.</p>

Elliptic-like regularization of a fully nonlinear evolution inclusion and applications

Consider in a Hilbert space [Formula: see text] the Cauchy problem [Formula: see text]: [Formula: see text], and associate with it the second-order problem [Formula: see text]: [Formula: see text], where [Formula: see text] is a (possibly set-valued) maximal monotone operator, [Formula: see text] is a Lipschitz operator, and [Formula: see text] is a positive small parameter. Note that [Formula: see text] is an elliptic-like regularization of [Formula: see text] in the sense suggested by Lions in his book on singular perturbations. We prove that the solution [Formula: see text] of [Formula: see text] approximates the solution [Formula: see text] of [Formula: see text]: [Formula: see text]. Applications to the nonlinear heat equation as well as to the nonlinear telegraph system and the nonlinear wave equation are presented.

On Lipschitz Perturbations of a Self-Adjoint Strongly Positive Operator

In this paper we study semilinear equations of the formAu+λF(u)=f, whereAis a linear self-adjoint operator, satisfying a strong positivity condition, andFis a nonlinear Lipschitz operator. As applications we develop Krasnoselskii and Ky Fan type approximation results for certain pair of maps and to illustrate the usability of the obtained results, the existence of solution of an integral equation is provided.

On constructive investigation of a class of non-linear boundary value problems for functional differential equations

We consider a two-point boundary value problem for a non-linear system of functional differential equations, for which a scheme of efficient investigation using certain iteration process is constructed. A new convergence condition is established in the case where a certain additional property of the Lipschitz operator is present, which may lead one to weaker assumptions.