Limits as p -> infinity of p-Laplacian problems with a superdiffusive power-type nonlinearity: Positive and sign-changing solutions

作者：Charro Fernando; Parini Enea^*

来源：Journal of Mathematical Analysis and Applications, 2010, 372(2): 629-644.

DOI：10.1016/j.jmaa.2010.07.005

• p-Laplacian
• Viscosity solution
• Morrey's estimate

We investigate the asymptotic behaviour as p -> infinity of sequences of solutions of the equation
{-Delta(p)u = lambda vertical bar u vertical bar(q(p)-2)u in Omega,
u = 0 on partial derivative Omega,
where lambda > 0 and q(p) > p with lim(p ->infinity) q(p)/p = Q >= 1. We are interested in the characterization of such limits as viscosity solutions of a PDE problem. Both positive and sign-changing solutions are considered.

• 出版日期2010-12-15