Özbekler, AbdullahAgarwal, Ravi P.Cetin, ErbilOzbekler, AbdullahMathematics2024-07-052024-07-05201721578-73031579-150510.1007/s13398-016-0290-62-s2.0-85009160760https://doi.org/10.1007/s13398-016-0290-6https://hdl.handle.net/20.500.14411/590Agarwal, Ravi P/0000-0003-0075-1704In 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.eninfo:eu-repo/semantics/closedAccessTime scaleLyapunov inequalityForcedMixed nonlinearSub-linearSuper-linearArticleQ1Q11111231246WOS:000392320300020