An Obstacle Problem in a Plane Domain with two Solutions

作者：Figueiredo Giovany M^*; Furtado Marcelo; Montenegro Marcelo

来源：Advanced Nonlinear Studies, 2014, 14(2): 327-337.

DOI：10.1515/ans-2014-0205

• obstacle problem
• exponential critical growth
• Trudinger-Moser inequality

We prove the existence of two nontrivial solutions for the variational inequality %26lt;br%26gt;integral(Omega) del u del(v - u) %26gt;= integral(Omega) f(u)(v - u) %26lt;br%26gt;for every nu belonging to some convex set, where Omega subset of R-2. The function f has critical exponential growth, in the sense that it behaves like exp(alpha(0)s(2)) as vertical bar s vertical bar -%26gt; infinity, for some alpha(0) %26gt; 0. We use variational methods for lower semicontinuous functionals.

• 出版日期2014-5