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Global Behavior of Positive Solutions of a Generalized Lane–Emden System of Nonlinear Differential Equations

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Abstract

In this paper we discuss the existence and the global behavior of positive solutions of the following generalized Lane–Emden system of differential equations:

$$\begin{aligned} -u''= & {} a(x)u^{\alpha }\,v^{r}\quad \text{ in } (0,1), \\ -v''= & {} b(x)u^{s}\,v^{\beta }\quad \, \text{ in } (0,1), \\ u'(0)= & {} v'(0)=0; \quad \, u(1)=v(1)=0, \end{aligned}$$

where \(r,\,s\in {\mathbb {R}}\), \(\alpha ,\,\beta <1\) such that \(\gamma :=(1-\alpha )(1-\beta )-rs>0\) and the nonnegative functions \(a,\,b\) satisfy some conditions related to the Karamata regular variation theory.

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  1. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203 , Jeddah, 21589, Saudi Arabia

    Ramzi S. Alsaedi

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  1. Ramzi S. Alsaedi
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Correspondence to Ramzi S. Alsaedi.

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Alsaedi, R.S. Global Behavior of Positive Solutions of a Generalized Lane–Emden System of Nonlinear Differential Equations. Mediterr. J. Math. 14, 81 (2017). https://doi.org/10.1007/s00009-017-0889-7

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  • DOI: https://doi.org/10.1007/s00009-017-0889-7

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