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Existence of infinitely many solutions for semilinear problems on exterior domains
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