Calculus of Variations and Geometric Measure Theory

G. Franzina - P. D. Lamberti

Existence and uniqueness for $p$-Laplacian nonlinear eigenvalue problems

created by franzina on 24 May 2012
modified on 06 Jun 2012


Published Paper

Inserted: 24 may 2012
Last Updated: 6 jun 2012

Journal: Elec. Journ. of Diff. Eqns.
Number: 26
Pages: 1-10
Year: 2010


We consider the Dirichlet eigenvalue problem $-\Delta_p u = \lambda \Vert u \Vert_{L^q(\Omega)}^{p-q} \vert u\vert^{q-2} u$ in the unknowns $u\in W_0^{1,p}(\Omega)$ (the eigenfunction) and $\lambda>0$ (the eigenvalue) on a domain of finite measure.

Keywords: p-laplacian, eigenvalue