Özbekler, AbdullahAgarwal, Ravi P.Ozbekler, AbdullahMathematics2024-07-052024-07-05201630096-30031873-564910.1016/j.amc.2016.02.0152-s2.0-84959422202https://doi.org/10.1016/j.amc.2016.02.015https://hdl.handle.net/20.500.14411/512Agarwal, Ravi P/0000-0003-0075-1704In this paper, we present some new Lyapunov and Hartman type inequalities for second order forced impulsive differential equations with mixed nonlinearities: x ''(t) + p(t)vertical bar x(t)vertical bar(beta-1)x(t) + q(t)vertical bar x(t)vertical bar(gamma-1)x(t) = f(t), t not equal theta(i); Delta x'(t) + p(i)vertical bar x(t)vertical bar(beta-1)x(t) + q(i)vertical bar x(t)vertical bar(gamma-1) x(t) = f(i), t = theta(i), where p, q, f are real-valued functions, {p(i)}, {q(i)}, {f(i)} are real sequences and 0 < gamma < 1 < beta < 2. No sign restrictions are imposed on the potential functions p, q and the forcing term f and the sequences {p(i)}, {q(i)}, {f(i)}. The inequalities obtained generalize and complement the existing results for the special cases of this equation in the literature. (C) 2016 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessLyapunov type inequalityMixed nonlinearSub-linearSuper-linearForcedImpulseReviewQ1282216225WOS:000371878200017