期刊论文

Hangzhou Hu<&wdkj&>Hangzhou Hu Hangzhou Hu Hangzhou Hu

英文

Mathematical Methods in the Applied Sciences

0170-4214

2023

46

5

5099-5118

10.1002/mma.8820

Supported in part by the China Postdoctoral Science Foundation (No. 2021M701365) and the funding of innovating activities in Science and Technology of Hubei Province. Supported in part by the National Natural Science Foundation of China (Nos. 12075102 and 11971212).

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We consider the following X‐ray free electron lasers Schrödinger equation (i∇−A)2u+V(x)u−μ|x|u=1|x|∗|u|2u−K(x)|u|q−2u,x∈ℝ3,$$ {\left(i\nabla -A\right)}&amp;#x0005E;2u&amp;#x0002B;V(x)u-\frac{\mu }{\mid x\mid }u&amp;#x0003D;\left(\frac{1}{\mid x\mid}\ast {\left&amp;#x0007C;u\right&amp;#x0007C;}&amp;#x0005E;2\right)u-K(x){\left&amp;#x0007C;u\right&amp;#x0007C;}&amp;#x0005E;{q-2}u,x\in {\mathbb{R}}&amp;#x0005E;3, $$ where A∈Lloc2(ℝ3,ℝ3)$$ A\in {L}_{loc}&amp;#x0005E;2\left({\mathbb{R}}&amp;#x0005E;3,{\mathbb{R}}&amp;#x0005E;3\right) $...