Browsing by Author "Yantir,A."

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    Citation - Scopus: 11
    Existence of Solutions of the Dynamic Cauchy Problem in Banach Spaces
    (Warsaw University, 2012) Cichon,M.; Kubiaczyk,I.; Sikorska-Nowak,A.; Yantir,A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
    In this paper we obtain the existence of solutions and Carathéodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales xδ(t) = f(t, x(t)), x(0) = x0, t 2 Ia, where f is continuous or f satisfies Carathéodory conditions and some conditions expressed in terms of measures of noncompactness. The Mönch fixed point theorem is used to prove the main result, which extends these obtained for real valued functions.
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    Citation - Scopus: 6
    Positive Solutions of a Second Order M-Point Bvp on Time Scales
    (2009) Topal,S.G.; Yantir,A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
    In this study, we are concerned with proving the existence of multiple positive solutions of a general second order nonlinear m-point boundary value problem (m-PBVP) uΔ∇(t) + a(t)uΔ(t) + b(t)u(t) + λh(t)f(t, u) = 0,t∈ [0,1], u(p(0))=0, u(σ(1)) Σm-2,i=1 α iu(ni),on time scales. The proofs are based on the fixed point theorems in a Banach space. We present an example to illustrate how our results work. © 2009 InforMath Publishing Group.