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

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.