Abstract
This paper concerns with the existence and regularity of solutions for the following Choquard type equation,
where \({I_\mu = \frac{1}{|x|^\mu}, 0 < \mu < 3}\), is the Riesz potential, \({F(s)}\) is the primitive of the continuous function f(s), and \({I_{\mu} * F(u)}\) denotes the convolution of \({I_{\mu}}\) and F(u). By using the variational method, we prove that problem (P), in the zero mass case, possesses at least a nontrivial solution under certain conditions on f.
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Research of C.O. Alves was partially supported by CNPq 304804/2017-7.
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Alves, C.O., Yang, J. Existence and Regularity of Solutions for a Choquard Equation with Zero Mass. Milan J. Math. 86, 329–342 (2018). https://doi.org/10.1007/s00032-018-0289-x
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DOI: https://doi.org/10.1007/s00032-018-0289-x