# American Institute of Mathematical Sciences

September  2010, 9(5): 1399-1410. doi: 10.3934/cpaa.2010.9.1399

## Uniqueness results for a Dirichlet problem with variable exponent

 1 Universität Zürich, Institut für Mathematik, CH-8057 Zürich, Switzerland

Received  September 2009 Revised  September 2009 Published  May 2010

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.
Citation: V. V. Motreanu. Uniqueness results for a Dirichlet problem with variable exponent. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1399-1410. doi: 10.3934/cpaa.2010.9.1399
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