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math.AP2016★ 453 cited
A guide to the Choquard equation
Vitaly Moroz, Jean Van Schaftingen
We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$ -Δu + V(x)u = \bigl(|x|^{-(N-α)} * |u|^p\bigr)|u|^{p - 2}…
math.AP2016★ 10 cited
Boundary singularities of solutions of semilinear elliptic equations in the half-space with a Hardy potential
Catherine Bandle, Moshe Marcus, Vitaly Moroz
We study a nonlinear equation in the half-space with a Hardy potential, specifically \[-Δu -\fracμ{x_1^2}u+u^p=0\quad\text{in}\quad \mathbb R^n_+,\] where and $-\…