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

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  08 January 2016

Giovany M. Figueiredo ,
Mateus Balbino Guimarães  and
Rodrigo da Silva Rodrigues
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)
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Abstract

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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.

Keywords

variational methodscritical exponentssingular perturbationsKirchhoff equationnonlinear elliptic equations

MSC classification

Secondary: 35A15: Variational methods 35B33: Critical exponents 35B25: Singular perturbations 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 4 , November 2016 , pp. 925 - 944
Copyright
Copyright © Edinburgh Mathematical Society 2016