Display Abstract

Title Higher-order effects in the boundary behavior of large radial solutions of polyharmonic equations with power nonlinearities

Name Paul G Schmidt
Country USA
Email pgs@auburn.edu
Co-Author(s) J.I. Diaz and M. Lazzo
Submit Time 2014-02-26 21:32:48
Session
Special Session 10: Nonlinear elliptic partial differential equations and systems
Contents
We study details of the boundary behavior of large radial solutions of semilinear elliptic equations involving the polyharmonic operator $\Delta^{\!m}$, power nonlinearities, and positive radial weights. Extending a known result for the case $m=1$, we obtain the first and second terms in the asymptotic expansions of all such solutions in the biharmonic case, $m=2$. For general $m$, we establish analogous expansions under additional conditions. We also describe situations in which these conditions fail and somewhat unexpected boundary behavior ensues.