Abstract
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.