Agarwal, Ravi P.Ozbekler, AbdullahMathematics2024-07-052024-07-05201681534-03921553-525810.3934/cpaa.20160372-s2.0-84990198570https://doi.org/10.3934/cpaa.2016037https://hdl.handle.net/20.500.14411/676Agarwal, Ravi P/0000-0003-0075-1704In the case of oscillatory potentials, we present Lyapunov type inequalities for nth order forced differential equations of the form x((n))(t) + Sigma(m)(j=1) qj (t)vertical bar x(t)vertical bar(alpha j-1)x(t)= f(t) satisfying the boundary conditions x(a(i)) = x(1)(a(i)) = x(11)(ai) = center dot center dot center dot = x((ki))(ai) = 0; i = 1, 2,..., r, where a(1) < a(2) < ... < a(r), 0 <= k(i) and Sigma(r)(j=1) k(j) + r = n: r >= 2. No sign restriction is imposed on the forcing term and the nonlinearities satisfy 0 < alpha(l) < ... < alpha a(j) < 1 < alpha a(j+1) < ... < alpha(m) < 2. The obtained inequalities generalize and compliment the existing results in the literature.eninfo:eu-repo/semantics/openAccessLyapunov type inequalityforcing termmixed nonlinearsub-linearsuper-linearArticleQ2Q315622812300WOS:000389636100014