Asymptotic analysis of positive solutions of third order nonlinear differential equations

作者：Jaros Jaroslav^*; Kusano Takasi; Tanigawa Tomoyuki

来源：Hiroshima Mathematical Journal, 2014, 44(1): 1-34.

DOI：10.32917/hmj/1395061555

• Third order nonlinear differential equation
• positive solutions
• asymptotic behavior
• regularly varying functions

It is shown that an application of the theory of regular variation (in the sense of Karamata) gives the possibility of determining the existence and precise asymptotic behavior of positive solutions of the third-order nonlinear differential equation (vertical bar x vertical bar(alpha-1)x %26apos;%26apos;)%26apos; + q(t)vertical bar x vertical bar(beta) x = 0, where alpha %26gt; beta %26gt; 0 are constants and q : [a, infinity) -%26gt; (0, infinity) is a continuous regularly varying function.

• 出版日期2014-3