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A VARIATIONAL APPROACH FOR A BI-NON-LOCAL ELLIPTIC PROBLEM INVOLVING THE p(x)-LAPLACIAN AND NON-LINEARITY WITH NON-STANDARD GROWTH

Published online by Cambridge University Press:  20 August 2013

FRANCISCO JULIO S. A. CORRÊA  and
AUGUSTO CÉSAR DOS REIS COSTA
FRANCISCO JULIO S. A. CORRÊA
Affiliation:
Centro de Ciências e Tecnologia, Unidade Acadêmica de Matemática e Estatística, Universidade Federal de Campina Grande, CEP:58.109-970, Campina Grande, Paraība, Brazil e-mail: [email protected]
AUGUSTO CÉSAR DOS REIS COSTA
Affiliation:
Instituto de Ciências Exatas e Naturais, Faculdade de Matemática, Universidade Federal do Pará, CEP:66075-110, Belém, Pará, Brazil e-mail: [email protected]
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Abstract

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In this paper we are concerned with a class of p(x)-Kirchhoff equation where the non-linearity has non-standard growth and contains a bi-non-local term. We prove, by using variational methods (Mountain Pass Theorem and Ekeland Variational Principle), several results on the existence of positive solutions.

Keywords

35J6035J7058E05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 2 , May 2014 , pp. 317 - 333
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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