In this paper, we investigate the existence of solutions for the fractional p-Laplace equation $$ (-\Delta)_{p}^{s}u+V(x) \vert u \vert ^{p-2}u=h_{1}(x) \vert u \vert ^{q-2}u+h_{2}(x) \vert u \vert ^{r-2}u \quad \mbox{in } \mathbb{R}^{N}, $$ where $N>sp$, $0< s<10$ and $h_{1}(x)$, $h_{2}(x)$ are allowed to change sign in $\mathbb {R}^{N}$. By using variant fountain theorem, we prove that the above equation admits infinitely many small and high energy solutions.

中文翻译：

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分数阶非线性分数p -Laplace方程的多重解。

在本文中，我们研究分数阶p-Laplace方程$$（-\ Delta）_ {p} ^ {s} u + V（x）\ vert u \ vert ^ {p-2} u解的存在性= h_ {1}（x）\ vert u \ vert ^ {q-2} u + h_ {2}（x）\ vert u \ vert ^ {r-2} u \ quad \ mbox {in} \ mathbb { R} ^ {N}，$$其中$ N> sp $，$ 0 <s <10 $和$ h_ {1}（x）$，$ h_ {2}（x）$允许更改$ \ mathbb {R} ^ {N} $中的符号。通过使用变体喷泉定理，我们证明了上面的等式允许无限多个小和高能解。