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Uniqueness results for a Dirichlet problem with variable exponent
We study the uniqueness of weak solutions for Dirichlet problems
with variable exponent and non-standard growth conditions. First, we provide
two uniqueness results under ellipticity type hypotheses. Next, we provide
a uniqueness result when the operator driving the problem is in the form of
the divergence of a monotone map. Finally, we derive a fourth uniqueness
result under homogeneity type hypotheses, by means of a comparison result
and approximation.