TY - JOUR
T1 - On the Radial Ground State of <em>p</em>-Laplacian Equation Involving Super-critical or Critical Exponents
AU - Benjin Xuan  & Zuchi Chen 
JO - Journal of Partial Differential Equations
VL - 3
SP - 193
EP - 206
PY - 2000
DA - 2000/08
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5506.html
KW - p-Laplacian equation
KW - super-critical exponents
KW - critical exponents
KW - radial ground state
KW - shooting argument
AB -  In this paper, we consider the existence and uniqueness of the radial ground state to the following p-Laplacian equation involving super-critical or critical exponents: Δ_pu + u^q - |Du|^σ = 0, x ∈ R^n, 2 ≤ p &lt; n, q ≥ [n(p - 1) + p]/(n - p), σ &gt; 0. Applying the shooting argument, the Schauder&#39;s fixed point theorem and some delicate estimates of auxiliary functions, we study the influence of the parameters n, p, q, σ on the existence and uniqueness of the radial ground state to the above p-Laplacian equation.