Radial Entire Solutions of Even Order Semilinear Elliptic Equations
Takaŝi Kusano, Manabu Naito, Charles A. Swanson · Canadian Journal of Mathematics · 1988
Semilinear elliptic partial differential equations of the type 1 will be considered throughout real Euclidean N-space, where m ≧ 2 is a positive integer, Δ denotes the N-dimensional Laplacian, and f is a real-valued continuous function in [0, ∞) × (0, ∞). Detailed hypotheses on the structure of f are listed in Section 3. Our objective is to prove the existence of radially symmetric positive entire solutions u(x) of (1) which are asymptotic to positive constant multiples of |x|2m−2i as |x| → ∞ for every i = 1,…, m, N ≧ 2i + 1.