Weak solutions of a hyperbolic-type partial dynamic equation in Banach spaces
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Date
2015
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AHMET YANTIR
Duygu SOYOĞLU
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Abstract
In this article we prove an existence theorem regarding the weak solu- tions to the hyperbolic-type partial dynamic equation z&,#915,&,#8710,(x y) = f(x y z(x y)) z(x 0) = 0 z(0 y) = 0 x &,#8712,T1 y &,#8712,T2 in Banach spaces. For this purpose by generalizing the de&,#64257,nitions and results of Cicho&,#324, et.al. we develop weak partial derivatives double integrability and the mean value results for double integrals on time scales. DeBlasi measure of weak noncompactness and Kubiaczyk s &,#64257,xed point theorem for the weakly sequentially continuous mappings are the essential tools to prove the main result. 2000 AMS Classi&,#64257,cation: 34G20 34N05 35L10 35R20 47N20 46B50.
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Bilgisayar Bilimleri- Teori ve Metotlar
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