On solvability for the second order nonlinear evolution equations with noncoercive W λ0-pseudomonotone maps.

In this paper, we consider a class of the second order evolution equations with W_λ0-pseudomonotone maps. Using the Faedo-Galerkin method, the resolvability for a class of evolution equations with nonlinear noncoercive operators, in particular with variation calculus operators, is proved. Furthermore, the uniform priori estimations in L_q (S;V'_σ) for derivatives are obtained. The results of the study suggest the perspectives for investigation of wider classes of wave processes with "nonlinear friction" as compared to [12, 13]. [ABSTRACT FROM AUTHOR]