Browsing by Author "Soyoğlu, Duygu"

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    Master Thesis
    Weak Solutions of Cauchy Dynamic and Hyperbolic Partial Dynamic Equations in Banach Spaces
    (2012) Soyoğlu, Duygu; Silindir, Ahmet Yantır
    In this dissertation, we obtain the sufficient conditions (as close as necessary conditions) for the existence of weak solutions for the second order dynamic Cauchy problem with mixed derivatives and an hyperbolic partial dynamic equation in Banach spaces. As the dynamic equations are the unification of differential, difference and q-discrete equations, our results are also true for the special cases R;Z; hZ and Kq.We establish integral operators corresponding to our problems in appropriate circumstances and we prove the existence of the fixed points of these operators via Sadowskii fixed point theorem. The measure of weak noncompactness ,introduced by DeBlasi, is used for the compactness condition of the operators.