Standing wave solutions for a Fisher type equation with a nonlocal convection (Q1096787)

The author considers the actual solvability of a nonlinear equation \(du_{xx}''-[(K*u)u]'+ku(1-u)=0.\) It is proved that there is no solution in C \(2(R)\cap L_ 1(R)\cap L_{\infty}(R)\) for kernels \(K(x)\in L_ 1(R)\), and that for some specific kernel \(K(x)\not\in L_ 1(R)\) there is a range of value of \(\int_{R}u dx\) over which such a solution exists.