Browsing by Author "Cetin, Erbil"

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    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.
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    Citation - WoS: 3
    Citation - Scopus: 3
    Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales
    (Springer-verlag Italia Srl, 2017) Agarwal, Ravi P.; Cetin, Erbil; Ozbekler, Abdullah
    In this paper, we present some newHartman and Lyapunov inequalities for second-order forced dynamic equations on time scales T with mixed nonlinearities: x(Delta Delta)(t) + Sigma(n)(k=1) qk (t)vertical bar x(sigma) (t)vertical bar (alpha k-1) x(sigma) (t) = f (t); t is an element of [t(0), infinity)(T), where the nonlinearities satisfy 0 < alpha(1) < ... < alpha(m) < 1 < alpha(m+1) < ... < alpha(n) < 2. No sign restrictions are imposed on the potentials qk, k = 1, 2, ... , n, and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.