TY - JOUR
T1 - Nontrivial Solutions for Some Semilinear Elliptic Equations with Critical Sobolev Exponents
AU - Wang Chuanfang, Xue Ruying
JO - Journal of Partial Differential Equations
VL - 1
SP - 77
EP - 96
PY - 1991
DA - 1991/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5763.html
KW - Semilinear elliptic equation
KW -  Sobolev exponent
KW -  Critical value
KW - Critical point
KW -  (P &#8226 S) condition
AB -  Let &#937 be a bounded domain in R^4(n &#8805 4) with smooth boundary &#8706&#937. We discuss the existence of nontrivial solutions of the Dirichlet problem {- &#916u = a(x) |u|^{4/(a-2)}u + &#955u + g(x, u), \quad x &#8712 &#937 u = 0, \quad x &#8712 &#8706&#937 where a(x) is a smooth function which is nonnegative on \overline{&#937} and positive somewhere, &#955> 0 and &#955 &#8713 &#963(-&#916). We weaken the conditions on a(x) that are generally assumed in other papers dealing with this problem.