The Cauchy problem in scale of Banach spaces with deviating variables



	The Cauchy problem in scale of Banach spaces with deviating variables


	Fixed Point Theory, Volume 22, No. 1, 2021, 219-230, February 1st, 2021 DOI: 10.24193/fpt-ro.2021.1.15 Authors: Nguyen Bich Huy and Pham Van Hien Abstract: In this paper, we first prove the existence and uniqueness results for the Cauchy problems in a scale of Banach spaces with deviating variables of the form u'(t)=F[t,A(t,u(t)),B(u(h(t)))]. We then apply it to study a Cauchy problem for PDEs in a Gevrey class with deviation at the derivatives. This extends some known results. Key Words and Phrases: Scale of Banach spaces, Cauchy problem, deviating variable, Gevrey function, fixed point. 2010 Mathematics Subject Classification: 35A10, 34G20, 58D25, 47H10. Published on-line: February 1st, 2021. Abstract pdf Fulltext pdf Back to volume's table of contents