Evolution inequalities with noncoercive w λ 0 -pseudomonotone volterra-type mappings
We consider a class of differential-operator inequalities with noncoercive w λ 0 -pseudomonotone operators. The problem of the existence of solutions of the Cauchy problem for these inequalities is investigated by using the Dubinsky method. A priori estimates for these solutions and their derivatives are obtained. We give a model example that illustrates the results and generalizations obtained.
English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 11, pp 1752-1777.
Citation Example: Kasyanov P. O., Mel'nik V. S. Evolution inequalities with noncoercive w λ 0 -pseudomonotone volterra-type mappings // Ukr. Mat. Zh. - 2008. - 60, № 11. - pp. 1499 – 1519.