TY - JOUR
T1 - On the Existence of Positive Solutions of Quasilinear Elliptic Equations with Mixed Boundary Conditions
AU - Xue Ruying
JO - Journal of Partial Differential Equations
VL - 3
SP - 61
EP - 71
PY - 1992
DA - 1992/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5745.html
KW - Critical point theory
KW -  quasilinear elliptic equation
KW -  mixed boundary condition
KW -  isoperimetric constant
AB -  In this paper, the existence of positive solutions for the mixed boundary problem of quasilinear elliptic equation {-div (|&#8711u|^{p-2}&#8711u) = |u|^{p^&#8727-2}u + f(x, u), \quad u > 0, \quad x &#8712 &#937 u|_&#915_0 = 0, \frac{&#8706u}{&#8706\overrightarrow{n}}|_&#915_1 = 0 is obtained, where &#937 is a bounded smooth domain in R^N, &#8706&#937 = \overrightarrow{&#915}_0 &#8746 \overrightarrow{&#915}_1, 2 &#8804 p < N, p^&#8727 = \frac{Np}{N-p}, &#915_0 and &#915_1 are disjoint open subsets of &#8706&#937.