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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
In this paper, the Hardy-Type inequality with more general weights is established in weighted variable exponent Sobolev spaces. With the help of it, existence of nontrivial weak solutions of the p(x)-Laplace type equations is proved.
Keywords:Weighted Variable Exponent Space, Hardy type inequality, p(x)-Laplace type operator, Mountain pass theorem