Abstract: In this talk, we investigate the existence of weak solutions for elliptic problems involving Choquard nonlinearity. These equations have attracted significant attention due to their ability to model long-range interactions in various real-world applications. A key concept in solving PDEs is that of weak solutions. These solutions satisfy the integral form of the PDE and are useful when classical solutions may not exist or are challenging to compute. This makes them exceedingly valuable in practical applications. We will use Variational methods to solve the PDEs. This technique essentially transforms the problem of solving a PDE into the problem of finding critical points of the associated functional.
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