In this paper, by using the topological degree theory for multivalued maps and the method of guiding functions, the existence and global bifurcation for periodic solutions of a class of differential variational inequalities are studied.

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Our aim is to study a new class of differential variational inequalities involving fractional derivatives. Using the fixed point approach, the existence of decay solutions to the mentioned problem is proved.

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The paper deals with a second order integro-partial differential equation in RnRn with a nonlocal, degenerate diffusion term. Nonlocal conditions, such as the Cauchy multipoint and the weighted mean value problem, are investigated. The existence of periodic solutions is also studied. The dynamic is transformed into an abstract setting and the results come from an approximation solvability method. It combines a Schauder degree argument with an Hartman-type inequality and it involves a Scorza-Dragoni type result. The compact embedding of a suitable Sobolev space in the corresponding Lebesgue space is the unique amount of compactness which is needed in this discussion. The solutions are located in bounded sets and they are limits of functions with values in finitely dimensional spaces

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An existence theorem for differential inclusions in Hilbert spaces with nonlocal conditions is proved. Periodic, anti-periodic, mean value and multipoint conditions are included in this study. The investigation is based on a combination of the approximation solvability method with Hartman-type inequalities. A feedback control problem associated to a first order partial differential equation completes this discussion