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

Keywords:

$p$-Laplacian with indefinite weight, principal eigencurve, principal eigenvalue, principal eigenfunction, stability $p$-Laplacian with indefinite weight, principal eigencurve, principal eigenvalue, principal eigenfunction, stability

MSC Classifications:

35P30, 35P60, 35J70 show english descriptions Nonlinear eigenvalue problems, nonlinear spectral theory
unknown classification 35P60
Degenerate elliptic equations 35P30 - Nonlinear eigenvalue problems, nonlinear spectral theory
35P60 - unknown classification 35P60
35J70 - Degenerate elliptic equations

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