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

Figure 3

Critical case: 𝑁=3, 𝑝=5. ((a), (c), and (e)) Homoclinic and periodic orbit solutions of (3.2) proved in Theorem 3.1. ((b), (d), and (f)) The corresponding solutions of (3.1) proved in Theorem 3.2: 𝑤₁(𝑟)=1/√2𝑟 is the known singular solution, 𝑤₂(𝑟) is a new positive singular solution, and 𝑤₃(𝑟) is a new sign changing singular solution.

(a)

(b)

(c)

(d)

(e)

(f)