Elsevier

Applied Mathematics Letters

Volume 48, October 2015, Pages 128-134
Applied Mathematics Letters

Asymptotic integration of second-order nonlinear delay differential equations

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Abstract

We study the asymptotic integration problem for second-order nonlinear delay differential equations of the form (p(t)x(t))+q(t)x(t)=f(t,x(g(t))). It is shown that if u and v are principal and nonprincipal solutions of equation (p(t)x)+q(t)x=0, then there are solutions x1(t) and x2(t) of the above nonlinear equation such that x1(t)=au(t)+o(u(t)),t and x2(t)=bv(t)+o(v(t)),t.

Keywords

Delay differential equations
Asymptotic integration
Fixed point theory
Principal and nonprincipal solutions

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Current address: American University of the Middle East, College of Engineering and Technology, Department of Mathematics & Statistics, Kuwait.