Existence and multiplicity of solutions for a supercritical elliptic problem in unbounded cylinders.

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dc.contributor.authorAssunção, Ronaldo Brasileiro
dc.contributor.authorMiyagaki, Olimpio Hiroshi
dc.contributor.authorRodrigues, Bruno Mendes
dc.date.accessioned2019-06-11T13:28:28Z
dc.date.available2019-06-11T13:28:28Z
dc.date.issued2017
dc.description.abstractWe consider the following elliptic problem: – div( |∇u| p–2∇u |y| ap ) = |u| q–2u |y| bq + f(x) in , u = 0 on ∂, in an unbounded cylindrical domain := (y,z) ∈ Rm+1 × RN–m–1;0< A < |y| < B < ∞ , where 1 ≤ m < N – p, q = q(a, b) := Np N–p(a+1–b) , p > 1 and A, B ∈ R+. Let p∗ N,m := p(N–m) N–m–p . We show that p∗ N,m is the true critical exponent for this problem. The starting point for a variational approach to this problem is the known Maz’ja’s inequality (Sobolev Spaces, 1980) which guarantees, for the q previously defined, that the energy functional associated with this problem is well defined. This inequality generalizes the inequalities of Sobolev (p = 2, a = 0 and b = 0) and Hardy (p = 2, a = 0 and b = 1). Under certain conditions on the parameters a and b, using the principle of symmetric criticality and variational methods, we prove that the problem has at least one solution in the case f ≡ 0 and at least two solutions in the case f ≡ 0, if p < q < p∗ N,m.pt_BR
dc.identifier.citationASSUNÇÃO, R. B.; MIYAGAKI, O. H.; RODRIGUES, B. M. Existence and multiplicity of solutions for a supercritical elliptic problem in unbounded cylinders. Boundary Value Problems, v. 2017, n. 52, p. 1-11, mar./abr. 2017. Disponível em: <https://boundaryvalueproblems.springeropen.com/articles/10.1186/s13661-017-0783-z>. Acesso em: 19 mar. 2019.pt_BR
dc.identifier.doihttps://doi.org/10.1186/s13661-017-0783-zpt_BR
dc.identifier.issn1687-2770
dc.identifier.urihttp://www.repositorio.ufop.br/handle/123456789/11516
dc.language.isoen_USpt_BR
dc.rightsabertopt_BR
dc.rights.licenseO periódico Boundary Value Problems permite o arquivamento da versão/PDF do editor no Repositório Institucional. Fonte: Sherpa/Romeo <http://www.sherpa.ac.uk/romeo/search.php?issn=1687-2762>. Acesso em: 20 out 2016.pt_BR
dc.subjectPositive solutionpt_BR
dc.subjectDegenerated operatorpt_BR
dc.subjectVariational methodspt_BR
dc.titleExistence and multiplicity of solutions for a supercritical elliptic problem in unbounded cylinders.pt_BR
dc.typeArtigo publicado em periodicopt_BR
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