Radially Symmetric Solutions of Δ𝑤+|𝑤|^𝑝−1𝑤=0

Figure 1

Subcritical example: 𝑁=3, 𝑝=4. ((a) and (b)) The unstable manifold (𝐴₁ and 𝐴₂) and stable manifold (𝐵₁ and 𝐵₂) lead from (0,0) into the (ℎ,ℎ^′) phase plane. ((c)–(f)) (c) and (e) show the ℎ components of solutions on 𝐴₁, 𝐴₂, 𝐵₁, 𝐵₂; (d) and (f) show corresponding solutions of (1.4): 𝑤₀ is generated by 𝐴₁, 𝑤₂(𝑟) is the new positive singular solution generated by 𝐵₁, and 𝑤₁(𝑟)=(2/9)^1/3𝑟^−2/3.

(a)

(b)

(c)

(d)

(e)

(f)