| Abstract: |
| I'll talk about the Rayleigh quotients with a parameter for the $p$-Laplacian. It is well known that critical values of the standard Rayleigh quotient corresponds to eigenvalues for the $p$-Laplacian. I introduce that our quotient with a parameter also exhibits similar characteristics as a nonlinear eigenvalue problem. Moreover, I'd like to show that critical points correspond to solutions for $p$-Laplace equation with polynomial nonlinearities by converting it effectively. |
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