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

  Published:2006-09-01
 Printed: Sep 2006
  • Abdelouahed El Khalil
  • Said El Manouni
  • Mohammed Ouanan
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Abstract

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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