Zhitao Zhang, Shujie Li, Shibo Liu, Weijie Feng, "On an asymptotically linear elliptic Dirichlet problem", Abstract and Applied Analysis, vol. 7, Article ID 825891, 8 pages, 2002. https://doi.org/10.1155/S1085337502207046
On an asymptotically linear elliptic Dirichlet problem
Under very simple conditions, we prove the existence of one positive and one negative solution of an asymptotically linear elliptic boundary value problem. Even for the resonant case at infinity, we do not need to assume any more conditions to ensure the boundness of the (PS) sequence of the corresponding functional. Moreover, the proof is very simple.
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