| Volume 15, Number 2, 2025, Pages - DOI：10.11948/JAAC-2024-0241 |
| Existence and concentration of solutions for discontinuous elliptic problems with critical growth |
| Ziqing Yuan |
| Keywords:Elliptic problem Concentration Variational method |
| Abstract: |
| This paper concerns the following elliptical problem with discontinuous nonlinearity
$$\aligned
\begin{cases}
-\epsilon^2\Delta u+V( x)u=f(u)+|u|^{2^*-2}u,~~x\in\R^N,\u>0,
\end{cases}
\endaligned$$
where $N\geq 3$, $\epsilon>0$ and $f(u)$ is a discontinuous function. We obtain the existence and concentration results of this problem. Our results generalize some recent results on this kind of problems. In order to obtain these results, a suitable truncation, concentration compactness principle, new analytic technique and variational method are used. |
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