In this work, we study the existence of solutions to the fractional-Choquard equation$$\begin{aligned} (-\Delta )^s_{\nu }u+V(x)|u|^{\nu -2}u=(I_{\alpha }*|u|^q)|u|^{q-2}u+h(u),\quad x\in {{\mathbb {R}}}^N, \end{aligned}$$(0.1)where \(\nu =\frac{N}{s}, 0<s<1, N\ge 2\), V(x) is a positive and bounded function in \({{\mathbb {R}}}^N\), \(I_{\alpha }\) is the Riesz potential, \(qs>N\) and the continuous function h(u) behaves like \(\exp (\alpha _0|u|^{\frac{N}{N-s}})\) growth. Using the symmetric rearrangement method with some special techniques and symmetric mountain pass lemma, we prove the existence of infinitely many solutions for (0.1) in \(W^{s,\nu }({\mathbb {R}}^N)\).

中文翻译：

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临界指数增长为$$ {\ mathbb {R}} ^ N $$ R N的分数次方方程的解的存在性

在这项工作中，我们研究分数Choquard方程$$ \ begin {aligned}（-\ Delta）^ s _ {\ nu} u + V（x）| u | ^ {\ nu -2}的解的存在性u =（I _ {\ alpha} * | u | ^ q）| u | ^ {q-2} u + h（u），\ quad x \ in {{\ mathbb {R}}} ^ N，\ end {aligned} $$（0.1）其中\（\ nu = \ frac {N} {s}，0 <s <1，N \ ge 2 \），V（x）是\（{ {\ mathbb {R}} ^ N \），\（I _ {\ alpha} \）是Riesz势，\（qs> N \）和连续函数h（u）的行为像\（\ exp（\ alpha _0 | u | ^ {\ frac {N} {Ns}}）\）增长。使用一些特殊技术的对称重排方法和对称的山口引理，我们证明了\（W ^ {s，\ nu}（{\ mathbb {R}} ^ N）\中（0.1）的无限多解的存在）。