Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity

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dc.contributor.authorRecova, Leandro L.
dc.contributor.authorRumbos, Adolfo J.
dc.date.accessioned2021-09-29T20:53:33Z
dc.date.available2021-09-29T20:53:33Z
dc.date.issued2020-06-16
dc.description.abstractIn 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent15 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationRecôva, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14567
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectSemilinear elliptic boundary value problem
dc.subjectSuperlinear subcritical growth
dc.subjectInfinite dimensional Morse theory
dc.subjectCritical groups
dc.titleExistence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity
dc.typeArticle

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