TY - JOUR
T1 - Positive Solution of a Semilinear Elliptic Equation on <em>R<sup>N</sup></em>
AU - Cao , Daomin
JO - Journal of Partial Differential Equations
VL - 3
SP - 261
EP - 272
PY - 1995
DA - 1995/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5658.html
KW - Elliptic equations
KW - positive solution
KW - critical point
AB -  In this paper, we obtain the existence of positive solution of {-Δu = b(x)(u - λ)^p_+,\qquad x ∈ R^N λ &gt; 0, |∇ u| ∈ L² (R^N),\qquad u ∈ L\frac{2N}{N-2} (R^N) under the assumptions that 1 &lt; p &lt; \frac{N+2}{N-2}, N ≥ 3, b(x) satisfies b(x) ∈ C(R^N), b(x) &gt; 0 in R^N b(x) →_{|x|→∞}b^∞ and b(x) &gt; \frac{4}{p+3}b^∞ for x ∈ R^N