A bijection is established between solutions of -Δ_p u = μ|u|^{q-2}u + |u|^{r-2}u and critical points of the generalized Rayleigh quotient R_α, and it is used to characterize degenerate and sign-changing solutions.
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On Rayleigh quotients connected to $p$-Laplace equations with polynomial nonlinearities
A bijection is established between solutions of -Δ_p u = μ|u|^{q-2}u + |u|^{r-2}u and critical points of the generalized Rayleigh quotient R_α, and it is used to characterize degenerate and sign-changing solutions.