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math.AP2022
Asymptotic profiles for a nonlinear Kirchhoff equation with combined powers nonlinearity
Shiwang Ma, Vitaly Moroz
We study asymptotic behavior of positive ground state solutions of the nonlinear Kirchhoff equation $$ -\Big(a+b\int_{\mathbb R^N}|\nabla u|^2\Big)Δu+ λu= u^{q-1}+ u^{p-1} \quad {\…
math.AP2022
Normalized solutions for the Choquard equation with mass supercritical nonlinearity
Na Xu, Shiwang Ma
We consider the nonlinear Choquard equation $$\begin{cases} & - Δu = (I_α\ast F(u))F'(u) -μu \ \text{in}\ \mathbb{R}^N, & u \in \ H^1(\mathbb{R}^N), \ \int_{\mathbb{R}^N} |u|^2 dx=…