| 摘要: |
| 本文研究$\mathbb{R}^N$上带有$p$-Laplacian算子的半正定问题:
\begin{equation*}
\left\{\begin{aligned}
-\Delta_p u &= h(x)(f(u)-a), & x\in\mathbb{R}^N, \u &> 0, & x\in\mathbb{R}^N,
\end{aligned}\right.
\end{equation*}
非线性项$f$ 满足在广义次临界增长的条件下, 研究上述方程解的存在性. |
| 关键词: 非光滑变分方法 拟线性椭圆方程 $p$-Laplacian 半正定问题 |
| DOI： |
| 分类号:35J35, 35B38, 35J92 |
| 基金项目: |
|
| Existence of Subcritical Positive Solutions for the Fractional $p$-Laplacian Choquard Logarithmic Equation via Nonsmooth Variational Methods |
|
Xinru Yao, Yongyi Lan
|
| Abstract: |
| This paper studies the semipositone problem with $p$-Laplacian operator in the whole
space $\mathbb{R}^N$:
\begin{equation}
\label{eq:main}
\left\{\begin{aligned}
-\Delta_p u &= h(x)(f(u)-a), & x\in\mathbb{R}^N, \u &> 0, & x\in\mathbb{R}^N,
\end{aligned}\right.
\tag{$P_a$}
\end{equation}
Under the condition that the nonlinear term $f$ satisfies a general subcritical growth, we
investigate the existence of solutions to the above equation. |
| Key words: Nonsmooth variational methods quasilinear elliptic equations $p$-Laplacian semipositone problems |
