Existence of infinitely many solutions for semilinear problems on exterior domains

Joseph Iaia, ,University of North Texas, Denton, TX 76203-1430, USA
2020 Communications on Pure and Applied Analysis  
In this paper we prove the existence of infinitely many radial solutions of ∆u + K(r)f (u) = 0 on the exterior of the ball of radius R > 0, B R , centered at the origin in R N with u = 0 on ∂B R and limr→∞ u(r) = 0 where N > 2, f is odd with f < 0 on (0, β), f > 0 on (β, ∞), f superlinear for large u and 0 < K(r) ≤ K 1 r α with 2 < α < 2(N − 1) for large r. 2020 Mathematics Subject Classification. Primary: 34B40; Secondary: 35B05.
doi:10.3934/cpaa.2020193 fatcat:eid5t4cuqjaibjtj53oz5jqjde