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On a fractional advection dispersion equation in \(\mathbb{R}^N\) involving a critical nonlinearity. (English) Zbl 1364.35011

Summary: In this paper, by using the variational principle of Ekeland, we prove the existence of at least one solution to the fractional advection dispersion equation in \(\mathbb{R}^N\).

MSC:

35A15 Variational methods applied to PDEs
34A08 Fractional ordinary differential equations
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
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