Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity
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In 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  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.
CitationRecôva, L. L., & Rumbos, A. J. (2020). Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity. Electronic Journal of Differential Equations, 2020(60), pp. 1-15.
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