Existence and Uniqueness of Solutions of Some Cauchy Problems for the Emden–Fowler Equation

Abstract

Abstract: We consider the Cauchy problem for the Emden–Fowler equation (Formula presented.) with parameters (Formula presented.) and (Formula presented.) for which the initial value of the solution belongsto one of the positive coordinate axes. Necessary and sufficient conditions on the parameters ofthe equation for the Cauchy problem with initial value on the positive ordinate axis to have asolution are obtained. (In this case, an improper initial value of the derivative of the solution isallowed.) The problem with initial value on the positive abscissa axis is shown to have a uniquesolution for (Formula presented.).