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Abstract: In this talk I survey some recent results related to a nonlinear eigenvalue problem driven by the p(x)- biharmonic operator {Δ(|Δu|^{p(x)−2}Δu) involving q(x)-Hardy inequality. The problem is considered in the variable exponent   Sobolev spaces W^{2,p(x)}(\Omega). Under some conditions on the function p(.) and q(.), we  prove the existence of at least one nondecreasing unbounded sequence of nonnegative eigenvalues. Moreover,  we prove that the domain \Omega satisfies the q(.)-Hardy-Rellich if and only if the first eigenvalue \lambda_1 is positive.