Linear equations of the Sobolev type with relatively \(p\)-radial operators (Q1386582)

The operator equation \[ L\dot u= Mu\tag{1} \] of Sobolev type is considered. The operators \(L\) and \(M\) are supposed to be linear and closed in Banach space \(U\). If the operator \(L^{-1}\) exists, the equation can be reduced to the standard form \(\dot u= Tu\). In the paper, the case \(\ker L\neq\{0\}\) is investigated.