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Solutions for a Kirchhoff Equation with Weight and Nonlinearity with Subcritical and Critical Caffarelli–Kohn–Nirenberg Growth

Published online by Cambridge University Press:  08 January 2016

Giovany M. Figueiredo
Affiliation:
Faculdade de Matemätica, Universidade Federal do Pará, CEP 6075-110, Belém, Pará, Brazil (giovany@ufpa.br)
Mateus Balbino Guimarães
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, CEP 13565-905, São Carlos, São Paulo, Brazil (mateusbalbino@yahoo.com.br; rodrigo@dm.ufscar.br)
Rodrigo da Silva Rodrigues
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, CEP 13565-905, São Carlos, São Paulo, Brazil (mateusbalbino@yahoo.com.br; rodrigo@dm.ufscar.br)

Abstract

In this paper we study the multiplicity of non-trivial solutions to a class of nonlinear boundary-value problems of Kirchhoff type. We prove existence results when the problem has nonlinearities with subcritical and with critical Caffarelli–Kohn–Nirenberg exponent.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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Solutions for a Kirchhoff Equation with Weight and Nonlinearity with Subcritical and Critical Caffarelli–Kohn–Nirenberg Growth
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