Existence and blow-up behavior of positive solutions to integral equations on bounded domains
Existence and blow-up behavior of positive solutions to integral equations on bounded domains
Consider the integral equation$ \begin{eqnarray*} f^{m-1}(x)+f^{q-1}(x) = \int_{\Omega}^{}\frac{f(y)}{\left | x-y \right |^{n-\alpha } }dy, \ \ \ \end{eqnarray*} $where $ 1<\alpha<n $, $ \Omega\subset{\mathbb{R}}^{n} $ is a smooth bounded domain. The existence of energy maximizing positive solutions in the subcritical case $ 2>q,m >\frac{2n}{n+\alpha} $, and the nonexistence of energy …