Positive entire solutions of inhomogeneous semilinear elliptic equations with supercritical exponent
Soohyun Bae - Hanbat National University, Daejeon 305-719, South Korea (email) Abstract: We establish that the elliptic equation $\Delta u + K(x)u^p + \mu f(x) = 0 in \mathbb{R}^n$ possesses a continuum of positive entire solutions under a set of assumptions on $K, p, \mu$ and $f$. When $K$ behaves like $1 + d|x|^( - q)$ near $\infty$ for some constants $d$ > 0 and $q$ > 0, separation and uncountable multiplicity of solutions appear for small $\mu$ > 0 provided that $n$ > 10, $p$ is large enough, and $f$ satisfies suitable decay conditions at $\infty$.
Keywords: Inhomogeneous semilinear elliptic equations, positive solutions, asymptotic behavior, uncountable multiplicity, separation.
Received: September 2004; Revised: March 2005; Published: September 2005. |