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On a nonlinear eigenvalue problem. (English) Zbl 0838.35094

Kilpeläinen, T. (ed.), Fall school in analysis, Jyväskylä, Finland, October 3-7, 1994. Jyväskylä: University of Jyväskylä. Ber., Univ. Jyväskylä, Math. Inst. 68, 33-54 (1995).
In this expository paper, the author considers the nonlinear eigenvalue problem \[ \text{div}(|\nabla u|^{p- 2} \nabla u)+ \lambda|u|^{p- 2} u= 0\quad\text{in } \Omega,\;u= 0\quad\text{on } \partial\Omega, \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\). Several known facts on eigenvalues and eigenfunctions for this problem are explained and some open problems in this area are mentioned.

MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J60 Nonlinear elliptic equations
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