Two Integrable Classes of Emden–Fowler Equations with Applications in Astrophysics and Cosmology
Two Integrable Classes of Emden–Fowler Equations with Applications in Astrophysics and Cosmology
Abstract We show that some Emden–Fowler (EF) equations encountered in astrophysics and cosmology belong to two EF integrable classes of the type <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mrow> <m:mrow> <m:mrow> <m:msup> <m:mi mathvariant="normal">d</m:mi> <m:mn>2</m:mn> </m:msup> <m:mi>z</m:mi> </m:mrow> <m:mo>/</m:mo> <m:mi mathvariant="normal">d</m:mi> </m:mrow> <m:msup> <m:mi>χ</m:mi> <m:mn>2</m:mn> </m:msup> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mi>A</m:mi> <m:msup> <m:mi>χ</m:mi> …