Consider the even-order nonlinear neutral differential equationand the associated differential inequalityUsing Lebesgue's dominated convergence theorem, a necessary and sufficient condition for the existence of eventually positive and bounded solutions is obtained.
In this paper we consider the existence, multiplicity, and nonexistence of positive periodic solutions forn-dimensional nonautonomous functional differential systemx'(t)=H(t,x(t))-λB(t)F(x(t-τ(t))), wherehiareω-periodic intand there existω-periodic functionsαi,βi∈C(R,R+)such thatαi(t)≤(hi(t,x)/xi)≤βi(t),∫0ωαi(t)dt>0,forx∈R+nall withxi>0,andt∈R,limxi→0+(hi(t,x)/xi)exist fort∈R;bi∈C(R,R+)areω-periodic functions and∫0ωbi(t)dt>0;fi∈C(R+n,R+),fi(x)>0forx >0;τ∈(R,R)is anω-periodic function. We show that the system has multiple or no positiveω-periodic solutions for sufficiently large or smallλ>0, respectively.
In this paper we consider the existence of nonoscillatory solutions of higher-order neutral differential equations with distributed coefficients and delays. We use the Banach contraction principle to obtain new sufficient condition for the existence of nonoscillatory solutions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.