Uniqueness of sign-changing radial solutions for Delta u - u plus vertical bar u vertical bar(p-1)u=0 in some ball and annulus

作者：Tanaka Satoshi^*

来源：Journal of Mathematical Analysis and Applications, 2016, 439(1): 154-170.

DOI：10.1016/j.jmaa.2016.02.036

• Scalar field equation
• Uniqueness
• Sign-changing radial solutions
• Modified Bessel functions

The following Dirichlet problem
[GRAPHICS]
is considered, where Omega is either an annulus or a ball in RN and p > 1. The uniqueness of radial solutions having exactly k 1 nodes is shown for the following cases: S2 is a sufficiently thin annulus; Omega is a certain small ball, N > 4 and 1 < p < NAN 2); Omega is the unit ball, N = 3 and 1 < p < 3; Omega is any annulus or any ball, but p > 1 is sufficiently close to 1 and N = 3, 5 or 7.

• 出版日期2016-7-1