Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation

作者：Jaros Jaroslav^*; Takasi Kusano; Manojlovic Jelena

来源：Central European Journal of Mathematics, 2013, 11(12): 2215-2233.

DOI：10.2478/s11533-013-0306-9

• Emden-Fowler differential equations
• Generalized regularly varying functions
• Regularly varying solutions
• Slowly varying solutions
• Asymptotic behavior of solutions
• Positive solutions

Positive solutions of the nonlinear second-order differential equation %26lt;br%26gt;(p(t)vertical bar x%26apos;vertical bar(alpha-1) x%26apos;)%26apos; + q(t)vertical bar x%26apos;vertical bar beta(-1) x = 0, alpha %26gt; beta %26gt; 0 %26lt;br%26gt;are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.

• 出版日期2013-12