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Asymptotic Analysis of Multiple Solutions for Perturbed Choquard Equations
Indian Journal of Pure and Applied Mathematics ( IF 0.7 ) Pub Date : 2020-03-13 , DOI: 10.1007/s13226-020-0389-5
Tao Wang

In this paper, we study the following Choquard equations with small perturbation f$$-\Delta u + V(x)u = (I_\alpha * |u|^p)|u|^{p-2}u+f(x), x\in \mathbb{R}^N.$$where N ≥ 3 and Iα denotes the Riesz potential. As is known that the above equation has a ground state uα and a bound state vα by fibering maps (see [22] or [23]), our aim is to show that for fixed \(p \in (1,\frac{N}{N-2})\), uα and vα converge to a ground state and a bound state of the limiting local problem respectively, as α → 0.

中文翻译:

扰动Choquard方程多重解的渐近分析。

在本文中,我们研究以下微扰动的Choquard方程f $$-\ Delta u + V(x)u =(I_ \ alpha * | u | ^ p)| u | ^ {p-2} u + f (X)中,x \在\ mathbb {R} ^ N。$$其中ñ ≥3和α表示中Riesz潜力。如已知的,上述方程具有接地状态ü α和束缚态v α由fibering图(见[22]或[23]),我们的目的是要表明,对于固定\(P \在(1,\压裂{N} {N-2})\) ù αv α收敛到基态和分别限制局部问题的束缚态,如α →交通0。
更新日期:2020-03-13
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