The Nehari manifold approach for singular equations involving the p(x)-Laplace operator

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We study the following singular problem involving the p(x)-Laplace operator , where is a nonconstant continuous function, Here, Ω is a bounded domain in with -boundary, λ is a positive parameter, are positive weight functions with compact support in Ω, and satisfy certain hypotheses () and (). We apply the Nehari manifold approach and some new techniques to establish the multiplicity of positive solutions for problem .