Recova, Leandro L.Rumbos, Adolfo J.2021-09-292021-09-292020-06-16Recôva, L. L., & Rumbos, A. J. (2020). Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity. <i>Electronic Journal of Differential Equations, 2020</i>(60), pp. 1-15.1072-6691https://hdl.handle.net/10877/14567In this article, we study the existence and multiplicity of solutions of the boundary-value problem -Δu = ƒ(x, u), in Ω, u = 0, on ∂Ω where ∆ denotes the N-dimensional Laplacian, Ω is a bounded domain with smooth boundary, ∂Ω, in ℝN (N ≯ 3), and ƒ is a continuous function having subcritical growth in the second variable. Using infinite-dimensional Morse theory, we extended the results of Furtado and Silva [9] by proving the existence of a second nontrivial solution under a non-quadradicity condition at infinity on the non-linearity. Assuming more regularity on the non-linearity ƒ, we are able to prove the existence of at least three nontrivial solutions.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalSemilinear elliptic boundary value problemSuperlinear subcritical growthInfinite dimensional Morse theoryCritical groupsArticle