带有上临界指数的Choquard方程的正规化解
首发时间:2023-12-22
摘要:本文研究了一类带有上临界指数的Choquard方程正规化解的存在性. 在一些适当的条件下, 通过山路引理和Pohoz\v{a}ev恒等式, 找到一个PS序列, 从而得到方程对应泛函的临界点, 证明了该方程的正规化解的存在性.
关键词: Choquard方程, 正规化解, 山路引理, Pohoz\v{a}ev恒等式
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Normalized solution to the Choquard equations with upper critical exponent
Abstract:In this paper,we study the existence of normal solutions of Choquard equations with upper critical exponent. Under some suitable conditions, we find a PS sequence through the mountain-pass lemma and Pohoz\v{a}ev identity, and then establish the critical point of the corresponding functional of the equation, and we prove the existence of the normal solution of the equation.
Keywords: Choquard Equation, Normalized Solution, Mountain-Pass Lemma, Pohoz\v{a}ev identity
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带有上临界指数的Choquard方程的正规化解
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