Existence for Nonoscillatory Solutions of Higher-Order Nonlinear Differential Equations

摘要

The existence of nonoscillatory solutions of the higher-order nonlinear differential equation[r(t)(x(t)+P(t)x(t-τ))(n-1)]′+∑i=1mQi(t)fi(x(t-σi))=0,  t≥t0, wherem≥1,n≥2are integers,τ>0,  σi≥0,  r,P,Qi∈C([t0,∞),R),  fi∈C(R,R)(i=1,2,…,m),is studied. Some new sufficient conditions for the existence of a nonoscillatory solution of above equation are obtained for generalQi(t)(i=1,2,…,m)which means that we allow oscillatoryQi(t)(i=1,2,…,m). In particular, our results improve essentially and extend some known results in the recent references.