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2005, 2005(Special): 50-59. doi: 10.3934/proc.2005.2005.50

Positive entire solutions of inhomogeneous semilinear elliptic equations with supercritical exponent

Soohyun Bae 1,

1. 

Hanbat National University, Daejeon 305-719, South Korea

Received  September 2004 Revised  March 2005 Published  September 2005

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: uncountable multiplicity, Inhomogeneous semilinear elliptic equations, asymptotic behavior, positive solutions, separation..
Mathematics Subject Classification: Primary: 35J60; Secondary: 35B05, 35B4.
Citation: Soohyun Bae. Positive entire solutions of inhomogeneous semilinear elliptic equations with supercritical exponent. Conference Publications, 2005, 2005 (Special) : 50-59. doi: 10.3934/proc.2005.2005.50
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