We consider a class of differential-operator inequalities with noncoercive \(w_{{{\rm{\lambda}}_{0}}}\)-pseudomonotone operators. The problem of existence of a solution of the Cauchy problem for these inequalities is investigated by the Dubinskii method. A priori estimates for these solutions and their derivatives are established. A model example illustrating the accumulated results is presented.
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Deceased (V. S. Mel’nyk).
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 11, pp. 1499–1519, November, 2008.
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Kas’yanov, P.O., Mel’nyk, V.S. Evolution inequalities with noncoercive \(w_{{{\rm{\lambda}}_{0}}}\)-pseudomonotone volterra-type mappings. Ukr Math J 60, 1752–1777 (2008). https://doi.org/10.1007/s11253-009-0167-3
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DOI: https://doi.org/10.1007/s11253-009-0167-3