Quadratic Integrability Of Solutions Of A Class Of Nonlinear Nth Order Differential Equations And Ou-Iang Type Inequalities

In this paper, the main results are:1. consider the nonlinear nth order differential equation :with the aid of an integral inequality, obtained some sufficient conditions which guarantee all solutions of equation(*)are bounded and belong to L2[0, oo).2. consider nth order difference equation:where r(k] = r(0) + with tne of a discrete inequal-ity,obtained sufficient conditions under which all solutions of equation (*) is quadratic convergent,and obtained the asymptotic behavior of equation(**).3.Some Ou-Iang type nonlinear integral inequalities defined on FT1 arc estab-lished,which are natural generalization and improvement of some known results obtained by E.H.Yang.4.Some Ou-Iang type discrete inequalities defined onNn are established,which arc natural generalization and improvment of some known results obtained by E.H.Yang.5. considered the follwing equation :where,r(t) > 0, =,p > 0,witb the aid of an Ou-Iang type integral in-equality,asmptotic behavior of solutions of the above equation are obtained.