Second order initial value problems of Lane-Emden type. (English) Zbl 1147.34300

Summary: This work discusses the existence of positive solutions to the initial value problem
\[ (py^{\prime })^{\prime }\pm pqg(y)=0, \quad t\in[0,T), \]
with \(y(0)=1\) and lim\(_{t\rightarrow 0^{+}}p(t)y^{\prime }(t)=0\). Our analysis is based on the Schauder-Tikhonov theorem.


34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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[1] Ames, W. F., Nonlinear Ordinary Differential Equations in Transport Processes (1968), Academic Press: Academic Press New York · Zbl 0193.04102
[2] Wong, J. S.W., On the generalized Emden-Fowler equations, SIAM Rev., 17, 339-360 (1975) · Zbl 0295.34026
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