On Rayleigh quotients connected to $p$-Laplace equations with polynomial nonlinearities

Vladimir Bobkov, Mieko Tanaka

Let $\Omega$ be a bounded open set and $p,q,r>1$. The main observation of the present work is the following: $W_0^{1,p}(\Omega )$-solutions of the equation $-{\Delta }_{p}u=\mu |u{|}^{q-2}u+|u{|}^{r-2}u$…