Asymptotic integration of second-order nonlinear differential equations via principal and nonprincipal solutions

作者：Ertem T^*; Zafer A

来源：Applied Mathematics and Computation, 2013, 219(11): 5876-5886.

DOI：10.1016/j.amc.2012.11.094

• Asymptotic integration
• Second-order
• Nonlinear
• Principal solution
• Nonprincipal solution

Let u and v denote respectively the principal and nonprincipal solutions of the second-order linear equation (p(t)x%26apos;)%26apos; + q(t)x = 0 defined on some half-line of the form [t(*), infinity). %26lt;br%26gt;It is shown that for any given real numbers a and b the nonlinear equation %26lt;br%26gt;(p(t)x%26apos;)%26apos; + q(t)x = f(t, x) %26lt;br%26gt;has a solution x(t) asymptotic to av(t) + bu(t) as t -%26gt; infinity under some reasonable conditions on the function f. Examples are given to illustrate the results.

• 出版日期2013-2-1