In this article, we will prove the existence of infinitely many positive weak solutions to the following nonlocal elliptic PDE.$$\begin{aligned} (-\Delta )^s u&= \frac{\lambda }{u^{\gamma }}+ f(x,u)\quad ~\text {in}\quad ~\Omega ,\\ u&=0~\quad \text {in}\quad ~\mathbb {R}^N{\setminus }\Omega , \end{aligned}$$where \(\Omega \) is an open bounded domain in \(\mathbb {R}^N\) with Lipschitz boundary, \(N>2s\), \(s\in (0,1)\), \(\gamma \in (0,1)\). We will employ variational techniques to show the existence of infinitely many weak solutions of the above problem.

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具有奇异性的非局部椭圆PDE的无穷多个解的存在性

在本文中，我们将证明以下非局部椭圆PDE的无穷多个正弱解的存在。$$ \ begin {aligned}（-\ Delta）^ s u＆= \ frac {\ lambda} {u ^ {\ gamma}} + f（x，u）\ quad〜\ text {in} \ quad〜\ Omega ，\\ u＆= 0〜\ quad \ text {in} \ quad〜\ mathbb {R} ^ N {\ setminus} \ Omega，\ end {aligned} $$其中\（\ Omega \）是一个开放式域在具有Lipschitz边界的\（\ mathbb {R} ^ N \）中，\（N> 2s \），\（s \ in（0,1）\），\（\ gamma \ in（0,1）\）。我们将使用变分技术来显示上述问题的无限多个弱解的存在。