## Ground state solutions of Pohožaev type and Nehari type for a class of nonlinear Choquard equations.(English)Zbl 1398.35071

Summary: In this paper, we study the autonomous Choquard equation $-\Delta u + u = (I_\alpha \ast F(u)) f(u), \,\, \text{in } \mathbb{R}^N,$ where $$N \geq 3$$, $$0 < \alpha < N$$, $$I_\alpha$$ is a Riesz potential, and $$f \in C(\mathbb{R}, \mathbb{R})$$ satisfies the general Berestycki-Lions conditions. In Sec. 2, combining constrained variational method with deformation lemma, we obtain a ground state solution of Pohožaev type for the above equation. In Sec. 3, using non-Nehari manifold method, we prove that the above equation has a ground state solution of Nehari type. The results improve some ones in [V. Moroz and J. van Schaftingen, Trans. Am. Math. Soc. 367, No. 9, 6557–6579 (2015; Zbl 1325.35052)].

### MSC:

 35J61 Semilinear elliptic equations

### Keywords:

nonlinear Choquard equations; ground state solutions

Zbl 1325.35052
Full Text:

### References:

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