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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...

Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs

Takeshi Fukao, Nobuyuki Kenmochi (2014)

Mathematica Bohemica

Recently, we established some generalizations of the theory of Lagrange multipliers arising from nonlinear programming in Banach spaces, which enable us to treat not only elliptic problems but also parabolic problems in the same generalized framework. The main objective of the present paper is to discuss a typical time-dependent double obstacle problem as a new application of the above mentioned generalization. Actually, we describe it as a usual parabolic variational inequality and then characterize...

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