Existence of mild solutions of a semilinear nonconvex differential inclusion with nonlocal conditions

Myelkebir Aitalioubrahim

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This note is concerned with the existence of mild solutions defined on a compact real interval for first and second order semilinear functional differential inclusions.

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∗Partially supported by Grant MM 409/94 of the Mininstry of Education, Science and Technology, Bulgaria. ∗∗Partially supported by Grants MM 521/95, MM 442/94 of the Mininstry of Education, Science and Technology, Bulgaria. The definition of the weak slope of continuous functions introduced by Degiovanni and Marzocchi (cf. [8]) and its interrelation with the notion “steepness” of locally Lipschitz functions are discussed. A deformation lemma and a mountain pass theorem for...