LAUSR

In this paper we discuss the existence and the global behavior of positive solutions of the following generalized Lane–Emden system of differential equations: $$\begin{aligned} -u''= & {} a(x)u^{\alpha }\,v^{r}\quad \text{ in } (0,1), \\ -v''= & {} b(x)u^{s}\,v^{\beta }\quad \, \text{ in } (0,1), \\ u'(0)= & {} v'(0)=0; \quad \, u(1)=v(1)=0, \end{aligned}$$-u′′=a(x)uαvrin(0,1),-v′′=b(x)usvβin(0,1),u′(0)=v′(0)=0;u(1)=v(1)=0,where $$r,\,s\in {\mathbb {R}}$$r,s∈R, $$\alpha ,\,\beta <1$$α,β<1 such that $$\gamma :=(1-\alpha )(1-\beta )-rs>0$$γ:=(1-α)(1-β)-rs>0 and the nonnegative functions $$a,\,b$$a,b satisfy some conditions related to the Karamata regular variation theory.