Título :	Kirchhoff elliptic problems with asymptotically linear or superlinear nonlinearities
Autor :	Furtado, Marcelo Fernandes Silva, Edcarlos D. Severo, Uberlandio B.
Assunto::	Equação de Kirchhoff Problemas assintoticamente lineares Problemas superlineares Métodos variacionais
Fecha de publicación :	14-oct-2020
Editorial :	Springer Nature
Citación :	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
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