For the third-order linear differential equations of the formr(t)x′′(t)′+p(t)x′(t)+q(t)x(t)=0, we will establish lower bounds for the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardy’s inequality and some generalizations of Opial and Wirtinger type inequalities.

No abstract

In this paper, we establish some lower bounds for the distance between zeros of nontrivial solutions or/and their derivatives and extend some results about distribution of zeros for a certain class of third-order differential equations of the form ðr 2 ðtÞðr 1 ðtÞx 0 ðtÞÞ 0 Þ 0 þ pðtÞx 0 ðtÞ þ qðtÞxðtÞ ¼ 0: The main results of this paper will be proved by employing some Hardy's and Opial's type inequalities.

For third order linear differential equations of the form r(t)x'(t)''+ p(t)x'(t) + q(t)x(t) = 0; we will establish lower bounds for the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardyís inequality, some generalizations of Opialís inequality and Boydís inequality.