On Solvability of Second-Order Semilinear Elliptic Equations on Spheres

The work concerns the solvability of one class of semilinear elliptic second-order differential equations on spheres of finite dimension in the class of weak solutions. These equations are inhomogeneous analogs of the stationary Fischer– Kolmogorov–Petrovsky–Piskunov equation and are essential both from applied and pure mathematical points of view.