It is well known that the loss of the coerciveness for governing monotone nonlinearities in evolution equations/inclusions can lead to the problem having no solution for given data, and the rule for choosing appropriate data has to be prescribed. Allowing constitutive functions in the evolution relations for elasto-/visco-plastic models of monotone type to be non-coercive, we first give a new (relaxed) meaning to the solvability of the systems of equations under consideration and then we define criteria for choosing admissible data, which guarantees the solvability in the defined sense. Realizing this strategy, a slight extension of the well-developed monotone-operator method to our needs is performed. The theory is applied to some well-known models in elasto-/visco-plasticity. The relations between the standard notion of the solvability and defined one are investigated.
Application of the mixed monotone operator method to fractional boundary value problems