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Agarwal, Ravi P.; Ertem, Türker; Zafer, Ağacık

Asymptotic integration of second-order nonlinear delay differential equations. (English) Zbl 1325.34083

Appl. Math. Lett. 48, 128-134 (2015).
Summary: 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 \(x_1(t)\) and \(x_2(t)\) of the above nonlinear equation such that \(x_1(t) = a u(t) + o(u(t)), t \to \infty\) and \(x_2(t) = b v(t) + o(v(t)), t \to \infty\).

Cited in 5 Documents

MSC:

34K25 Asymptotic theory of functional-differential equations
47N20 Applications of operator theory to differential and integral equations

Keywords:

delay differential equations; asymptotic integration; fixed point theory; principal and nonprincipal solutions
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References:

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