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In this article we study a class of nonlinear elliptic equations with variable exponents. We obtain an L 1 estimate on the solutions and prove the existence of weak solutions to such problems.

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In this paper we study a class of nonlinear parabolic problems with p(x, t) growth conditions. We prove the existence and uniqueness of bounded solutions to such a problem, with less constraint to p(x, t). Our results are generalizations of the corresponding results in the constant exponent case.

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