Abstract:

In this paper, authors consider the existence, uniqueness and nonexistence of
the radial ground state to the following p-Laplacian equation:
pu+uq−|Du| = 0, x 2
Rn, where 2  p < n, q is subcritical exponent, i.e. q < p − 1 = [n(p − 1) + p]/(n − p),
 > 0. Applying the shooting argument, Schauder’s fixed point theorem and some delicate
estimates of auxillary funtions, they study the influence of the parameters n, p, q,  > 0
on the existence, uniqueness and nonexistence of the radial ground state to the above
p-Laplacian equation.

Key words: p-Laplacian equation, radial ground state, shooting argument