ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

ThemainpurposeofthispaperistoextendandimprovesomeoftheresultsofSighandKusano4]forequationtothefollowingmoregeneraldifferentialequationoftheformwheren32andL0x(t)=x(t),LKx(t)=1≤k≤n.pi,gandf:a,∞)→RandH:a,∞)xRn→Rarecontinuousfunctionswithpi(t)>0,1≤i≤(n-1),pn(t)=1,andg(t)→∞ast→∞.ThedomainD(L.)ofL,,isdefinedtobethesetofallfunctionsx:Tx,co)-RsuchthatLix(t),05i5nexistandarecontinuousonTx,co).Inwhatfollowsbyasolutionof(2)wemeanthatafunctionxED(L.)whichsatisfies(2)forallsufficien…