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Title: Kirchhoff elliptic problems with asymptotically linear or superlinear nonlinearities
Authors: Furtado, Marcelo Fernandes
Silva, Edcarlos D.
Severo, Uberlandio B.
Assunto:: Equação de Kirchhoff
Problemas assintoticamente lineares
Problemas superlineares
Métodos variacionais
Issue Date: 14-Oct-2020
Publisher: Springer Nature
Citation: FURTADO, Marcelo F.; SILVA, Edcarlos D.; SEVERO, Uberlandio B. Kirchhoff elliptic problems with asymptotically linear or superlinear nonlinearities. Zeitschrift für angewandte Mathematik und Physik, v. 71, 186, 2020. DOI: https://doi.org/10.1007/s00033-020-01414-5.
Abstract: We establish the existence and multiplicity of solutions for Kirchhoff elliptic problems of type −m (∫R3|∇u|2dx) |Δu=f(x,u), x∈R3, where m:R+→R is continuous, positive and satisfies appropriate growth and/or monotonicity conditions. We consider the cases that f is asymptotically 3−linear or 3−superlinear at infinity, in an appropriated sense. By using variational methods, we obtain our results under crossing assumptions of the functions m and f with respect to limit eigenvalues problems. In the model case m(t)=a+bt, we also prove a concentration result for some solutions when b→0+.
DOI: https://doi.org/10.1007/s00033-020-01414-5
metadata.dc.relation.publisherversion: https://link.springer.com/article/10.1007/s00033-020-01414-5
Appears in Collections:IF - Artigos publicados em periódicos
MAT - Artigos publicados em periódicos

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