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| In this talk we consider the existence of weak solutions for equations driven by a non-local integrodifferential operator with an asymmetric nonlinear term. As a particular case, we derive existence results for the asymmetric fractional Laplace equations. By using variational methods in an appropriate abstract framework developed by Servadei and Valdinoci, we investigate the existence, nonexistence and uniqueness of weak solutions for the aforementioned equations. Our results extend some classical results for asymmetric elliptic boundary value problems to the non-local fractional setting. |
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