EXISTENCE AND CONCENTRATION OF SOLUTIONS FOR DISCONTINUOUS ELLIPTIC PROBLEMS WITH CRITICAL GROWTH

This paper concerns the following elliptical problem with discontinuous nonlinearity <p class="disp_formula">$\left\{\begin{array}{l}-\epsilon^2 \Delta u+V(x) u=f(u)+|u|^{2^*-2} u, \quad x \in \mathbb{R}^N, \\u&gt;0,\end{array}\right.$ where <i>N</i> ≥ 3, <i>ε</i> &gt; 0 and <i>f</i>(<i>u</i>) 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.