On the Principal Eigencurve of the p-Laplacian: Stability Phenomena

Khalil, Abdelouahed El ; Manouni, Said El ; Ouanan, Mohammed

Canadian mathematical bulletin, Tome 49 (2006) no. 3, pp. 358-370

Résumé

We show that each point of the principal eigencurve of the nonlinear problem $$-{{\Delta }_{p}}u-\text{ }\lambda m(x){{\left| u \right|}^{p-2}}u=\mu {{\left| u \right|}^{p-2}}u\,\,\text{in}\Omega ,$$ is stable (continuous) with respect to the exponent $p$ varying in $\left( 1,\infty\right)$ ; we also prove some convergence results of the principal eigenfunctions corresponding.

Détail

DOI : 10.4153/CMB-2006-036-5

Mots-clés : 35P30, 35P60, 35J70, p-Laplacian with indefinite weight, principal eigencurve, principal eigenvalue, principal eigenfunction, stability

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