General solutions of weakened equations in terms of stresses in the theory of elasticity

The general solutions of some weakened systems of equations expressed in terms of stresses in the isotropic theory of elasticity are analyzed. These systems are not equivalent to the classical one and involve the equilibrium equations and only three of the six equations of compatibility (either diagonal or off-diagonal ones). In the framework of elasticity theory, an equivalence of the formulations of quasistatic boundary value problems based on such systems and expressed in terms of stresses is discussed.