Browsing by Author "Cetin, Erbil"
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Article Citation Count: 4Existence of positive solutions of a Sturm-Liouville BVP on an unbounded time scale(Taylor & Francis Ltd, 2008) Yantır, Ahmet; Yantir, Ahmet; Cetin, Erbil; MathematicsA 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.Article Citation Count: 2Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales(Springer-verlag Italia Srl, 2017) Özbekler, Abdullah; Cetin, Erbil; Ozbekler, Abdullah; MathematicsIn 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.