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Abstract inclusions in Banach spaces with boundary conditions of periodic type

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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
⎧ $x ∈ S(x(0), sel_{F}(x))$

⎩ x (T) = x(0),
where, $F:[0,T] × 𝓚 → 2^E \∅$ is a multivalued map with convex compact values, 𝓚 ⊂ E, $sel_{F}$ is the superposition operator generated by F, and S: 𝓚 × L¹([0,T];E) → C([0,T]; 𝓚 ) an abstract operator. As an application, some results are given to the periodic boundary value problem for nonlinear differential inclusions governed by m-accretive operators generating not necessarily a compact semigroups.
  • Faculty of Mathematics and Informatics, Ibn Khaldoun University, 14000 Tiaret, Algeria
  • Faculty of Mathematics and Informatics, Ibn Khaldoun University, 14000 Tiaret, Algeria
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