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

Abstract: Let u and v denote respectively the principal and nonprincipal solutions of the second-order linear equation defined on some half-line of the form . It is shown that for any given real numbers a and b the nonlinear equationhas a solution asymptotic to as under some reasonable conditions on the function f. Examples are given to illustrate the results. [Copyright &y& Elsevier]