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http://dx.doi.org/10.4134/BKMS.2015.52.2.421

NONLINEAR DIFFERENTIAL INCLUSIONS OF SEMIMONOTONE AND CONDENSING TYPE IN HILBERT SPACES  

Abedi, Hossein (Department of Mathematical Sciences University of Kashan)
Jahanipur, Ruhollah (Department of Mathematical Sciences University of Kashan)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.2, 2015 , pp. 421-438 More about this Journal
Abstract
In this paper, we study the existence of classical and generalized solutions for nonlinear differential inclusions $x^{\prime}(t){\in}F(t,x(t))$ in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces. Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.
Keywords
differential inclusions; set-valued integral; semimonotone and hemicontinuous multifunctions; condensing multifunctions;
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