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Citation - WoS: 17
Citation - Scopus: 19
Weak Solutions for the Dynamic Cauchy Problem in Banach Spaces
(Pergamon-elsevier Science Ltd, 2009) Cichon, Mieczyslaw; Kubiaczyk, Ireneusz; Sikorska-Nowak, Aneta; Yantir, Ahmet
This paper is devoted to unify and extend the results of the existence of the weak solutions of continuous and discrete Cauchy problem in Banach spaces. We offer the existence of the weak solution of dynamic Cauchy problem on an infinite time scale. The measure of weak noncompactness and the fixed point theorem of Kubiaczyk are used to prove the main result. (C) 2009 Elsevier Ltd. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 4
Existence of Positive Solutions of a Sturm-Liouville Bvp on an Unbounded Time Scale
(Taylor & Francis Ltd, 2008) Topal, S. Gulsan; Yantir, Ahmet; Cetin, Erbil
A fixed point theorem of Guo-Krasnoselskii type is used to establish existence results for the nonlinear Sturm-Liouville dynamic equation (p(t)x(Delta))(del) + lambda phi(t)f(t,x(t)) = 0 with the boundary conditions on an unbounded time scale. Later on the positivity and the boundedness of the solutions are obtained by imposing some conditions on f.