Asymptotic behavior at infinity for solutions of Emden-Fowler type equations

Abstract

The semilinear equation Δu = |u|σ−1u is considered in the exterior of a ball in ℝn, n ≥ 3. It is shown that if the exponent σ is greater than a “critical” value (= n/n−2), then for x → ∞ the leading term of the asymptotics of any solution is a linear combination of derivatives of the fundamental solution. It is shown that there exist solutions with the indicated leading term of an asymptotics of such a type.