Asymmetric superlinear problems under strong resonance conditions

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dc.contributor.authorRecova, Leandro L.
dc.contributor.authorRumbos, Adolfo J.
dc.date.accessioned2022-06-03T14:58:13Z
dc.date.available2022-06-03T14:58:13Z
dc.date.issued2017-06-23
dc.description.abstractWe study the existence and multiplicity of solutions of the problem -∆u = -λ1u‾ + g(x, u), in Ω; u = 0, on ∂Ω, where Ω is a smooth bounded domain in ℝN (N ≥ 2), u‾ denotes the negative part of u : Ω → ℝ, λ1 is the first eigenvalue of the N-dimensional Laplacian with Dirichlet boundary conditions in Ω, and g : Ω x ℝ → ℝ is a continuous function with g(x, 0) = 0 for all x ∈ Ω. We assume that the nonlinearity g(x, s) has a strong resonant behavior for large negative values of s and is superlinear, but subcritical, for large positive values of s. Because of the lack of compactness in this kind of problem, we establish conditions under which the associated energy functional satisfies the Palais-Smale condition. We prove the existence of three nontrivial solutions of problem (1) as a consequence of Ekeland's Variational Principle and a variant of the mountain pass theorem due to Pucci and Serrin [14].
dc.description.departmentMathematics
dc.formatText
dc.format.extent27 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationRecova, L., & Rumbos, A. (2017). Asymmetric superlinear problems under strong resonance conditions. Electronic Journal of Differential Equations, 2017(149), pp. 1-27.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15842
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, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectStrong resonance
dc.subjectPalais-Smale condition
dc.subjectEkeland's principle
dc.titleAsymmetric superlinear problems under strong resonance conditionsen_US
dc.typeArticle

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