SOME REMARKS ON THE EQUATION FOR VARYING λ, p AND VARYING DOMAINS*

ABSTRACT

We consider positive solutions of the equation with Dirichlet boundary conditions in a smooth bounded domain Ω for λ > 0 and p > 1. We study the behavior of the solutions for varying λ, p and varying domains Ω in different limiting situations.

*This research was supported by MURST project “Metodi Variazionali ed Equazioni Differenziali non Lineari”. A.M. is supported by a Fulbright fellowship for the academic year 2000–2001.

Keywords:

• AMS Subject Classification: 35J60
• 35B30
• 35B40

Acknowledgments

Notes

*This research was supported by MURST project “Metodi Variazionali ed Equazioni Differenziali non Lineari”. A.M. is supported by a Fulbright fellowship for the academic year 2000–2001.