## A note on the nonlinear Rayleigh quotient.(English)Zbl 0805.35085

Gyllenberg, Mats (ed.) et al., Analysis, algebra, and computers in mathematical research. Proceedings of the 21st Nordic congress of mathematicians, Luleå Univ. of Technology, Sweden, 1992. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 156, 223-231 (1994).
Summary: The “power concavity” of the first eigenfunction to the equation $\text{div} \bigl( | \nabla u |^{p-2} \nabla u \bigr) + \lambda | u |^{p-2} u=0$ is studied in a ball. An introduction to this nonlinear eigenvalue problem is given. A conjecture is made, in particular, for the equation $$\Delta u + \lambda u = 0$$.
For the entire collection see [Zbl 0796.00012].

### MSC:

 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35J70 Degenerate elliptic equations

### Keywords:

concavity; first eigenfunction