Positive solutions of super-critical elliptic equations and asymptotics. (English) Zbl 0793.35029
Summary: This paper is devoted to the study of positive solutions of semilinear elliptic equations
\[
\Delta u+K(| x |)u^ p=0,\quad \text{ for }\quad p>{n+2 \over n-2},\quad \text{ and }\quad n \geq 3.
\]
Asymptotic behavior of ground states and uniqueness of singular ground states are proved via invariant manifold theory of dynamical systems. The Dirichlet problem in exterior domains is also studied. It is proved that this problem has one positive solution with fast decay and infinitely many positive solutions with slow decay. The asymptotics of the singular sequence of fast decay solutions when \(p\) approaches to \({n+2 \over n-2}\) is also discussed.
Keywords:
radial solutions; asymptotic behavior; semilinear elliptic equations; singular ground states; invariant manifold; exterior domainsReferences:
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