Linear instability of entire solutions for a class ofnon-autonomous elliptic equations

摘要

We study the effect of the potential |y~α on the stability of entire solutions for elliptic equations on R~N, N≥2, with exponential or smoooth/singular polynomial nonlinearities. Instability properties are crucial in order to establish regularity of theextrema] solution to some related Dirichlet nonlinear eigenvalue problem on boundeddomains. As a by-product of our results, we will improve the known results about theregularity of such solutions.