On Solvability of Operator Inclusions: Application to Elliptic Problems with the Neumann Boundary Condition

In studying the surjectivity of set-valued mappings, a modification of the acute-angle lemma (or the equilibrium theorem) is used. This allows one to weaken the coerciveness condition. Some applications to differential equations (inclusions) with Neumann boundary conditions are considered on Sobolev spaces W _p ¹() in which operators are used that are not coercive in the classical sense.