Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity
Date
2020-06-16
Authors
Recova, Leandro L.
Rumbos, Adolfo J.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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 [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.
Description
Keywords
Semilinear elliptic boundary value problem, Superlinear subcritical growth, Infinite dimensional Morse theory, Critical groups
Citation
Recôva, 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.
Rights
Attribution 4.0 International