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Abstract inclusions in Banach spaces with boundary conditions of periodic type

Lahcene Guedda, Ahmed Hallouz (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study in the space of continuous functions defined on [0,T] with values in a real Banach space E the periodic boundary value problem for abstract inclusions of the form ⎧ x S ( x ( 0 ) , s e l F ( x ) ) ⎨ ⎩ x (T) = x(0), where, F : [ 0 , T ] × 2 E is a multivalued map with convex compact values, ⊂ E, s e l F is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) an abstract operator. As an application, some results are given to the periodic boundary value problem for nonlinear differential inclusions governed by m-accretive...

An Iterative Procedure for Solving Nonsmooth Generalized Equation

Marinov, Rumen Tsanev (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 47H04, 65K10.In this article, we study a general iterative procedure of the following form 0 ∈ f(xk)+F(xk+1), where f is a function and F is a set valued map acting from a Banach space X to a linear normed space Y, for solving generalized equations in the nonsmooth framework. We prove that this method is locally Q-linearly convergent to x* a solution of the generalized equation 0 ∈ f(x)+F(x) if the set-valued map [f(x*)+g(·)−g(x*)+F(·)]−1 is Aubin continuous...

Eigenvalue results for pseudomonotone perturbations of maximal monotone operators

In-Sook Kim, Jung-Hyun Bae (2013)

Open Mathematics

Let X be an infinite-dimensional real reflexive Banach space such that X and its dual X* are locally uniformly convex. Suppose that T: X⊃D(T) → 2X* is a maximal monotone multi-valued operator and C: X⊃D(C) → X* is a generalized pseudomonotone quasibounded operator with L ⊂ D(C), where L is a dense subspace of X. Applying a recent degree theory of Kartsatos and Skrypnik, we establish the existence of an eigensolution to the nonlinear inclusion 0 ∈ T x + λ C x, with a regularization method by means...

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