Existence of Solutions for Semilinear Nonlocal Elliptic Problems via a Bolzano Theorem
In this paper we deal with the existence of positive solutions for the following nonlocal type of problems $$\everymath{\displaystyle} \left\{ \begin{array}{l@{\quad}l} -\Delta u = \frac{\sigma}{( \int_{\varOmega} g(u)\, dx )^p} f(u) & \mbox{in}\ \varOmega, \\[3mm] u>0 & \mbox{in}\ \varOmega, \\[1mm] u=0 & \mbox{on}\ \partial\varOmega, \end{array} \right. $$ where ? is a bounded smooth domain in ? N (N?1), f,g are continuous positive functions, ?>0 and p??.
semilinear elliptic equations nonlocal equations bifurcation methods 35j61 35b32