On the generalized weak Harnack inequality for non-negative super-solutions of quasilinear elliptic equations with absorption term

We prove the generalized weak Harnack inequality for non-negative super-solutions to quasi- linear elliptic equations with the generalized Orlicz growth

\(\text {div}\left({\mathit \Phi} \left(x\left|\nabla u\right|\right)\frac{\nabla u}{{\left|\nabla u\right|}^{2}}\right)=b\left(x\right)f\left(u\right), b\left(x\right)\ge 0.\) $$\text{div}\left(\mathrm{\Phi },\left(x,\left|\mathrm{\nabla },u\right|\right),\frac{\mathrm{\nabla }u}{{\left|\mathrm{\nabla },u\right|}^2}\right)=b\left(x\right)f\left(u\right),b\left(x\right)\ge 0.$$