Existence of infinitely many solutions for singular semilinear problems on exterior domains
Texas State University, Department of Mathematics
In this article we prove the existence of infinitely many radial solutions of ∆u + K(r)ƒ(u) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in ℝN with u = 0 on ∂BR and lim r→∞ u(r) = 0 where N > 2, ƒ is odd with ƒ < 0 on (0, β), ƒ < 0 on (β, ∞), ƒ is superlinear for large u, ƒ(u) ~ -1/(|u|q-1u) with 0 < q < 1 for small u, and 0 < K(r) ≤ K1/rα with N + q(N - 2) < α < 2(N - 1) for large r.
Exterior domain, Semilinear, Singular, Superlinear, Radial solution
Iaia, J. A. (2019). Existence of infinitely many solutions for singular semilinear problems on exterior domains. <i>Electronic Journal of Differential Equations, 2019</i>(108), pp. 1-11.