الفهرس | Only 14 pages are availabe for public view |
Abstract In this thesis, we discuss the oscillatory behavior of solutions of the third order mixed neutral di erential equation a(t) b(t) (x(t) + p1(t)x( 1(t)) + p2(t)x( 2(t)))0 0 0 + q(t)f( x(t) + p1(t)x( 1(t)) + p2(t)x( 2(t))) = 0; t t0; where is a non-negative constant and is the ratio of two odd positive integers. We introduce new su cient conditions for oscillation of solutions of the follow- ing forced third order di erential equation a(t) b(t) (x(t) + p1(t)x( 1(t)) + p2(t)x( 2(t))) 0 0 0 + q(t)f( x(t) + p1(t)x( 1(t)) + p2(t)x( 2(t))) = h(t); t t0; where h(t) 2 C ([t0;1);R). Moreover, we study the oscillatory behavior of solutions of the nonlinear third order di erential equation a(t) ” x(t) + Xn j=1 pj(t)x( j(t)) !00# !0 + Xm i=1 fi (t; x( i(t))) = 0; t t0; where 1R t0 a 1 (t)dt = 1 or 1R t0 a 1 (t)dt < 1. The obtained results improve and extend some known results in the literature. We give some examples that satisfy our results. |