caa a22 4500 605523495 CHVBK 20210128100749.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10958-015-2550-y doi (NATIONALLICENCE)springer-10.1007/s10958-015-2550-y Voitovich Mikhail Institute of Mathematics of the NAS of Ukraine, 3, Tereshchenkovskaya Str., 01601, Kiev, Ukraine aut On the existence of bounded generalized solutions of the Dirichlet problem for a class of nonlinear high-order elliptic equations [Elektronische Daten] [Mikhail Voitovich] In this article, we consider a class of nonlinear high-order elliptic equations with principal coefficients satisfying a strengthened coercivity condition, and with the lower-order term admitting an arbitrary growth with respect to unknown function and the growth rates of derivatives of this function coinciding with the exponents of the corresponding energy space. We prove a theorem on existence of bounded generalized solutions of the Dirichlet problem for equations of the given class. Springer Science+Business Media New York, 2015 Nonlinear high-order elliptic equations nationallicence strengthened coercivity nationallicence Dirichlet problem nationallicence generalized solution nationallicence L ∞ -estimate of a solution nationallicence Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/1(2015-10-01), 86-113 1072-3374 210:1<86 2015 210 10958 https://doi.org/10.1007/s10958-015-2550-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2550-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Voitovich Mikhail Institute of Mathematics of the NAS of Ukraine, 3, Tereshchenkovskaya Str., 01601, Kiev, Ukraine aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/1(2015-10-01), 86-113 1072-3374 210:1<86 2015 210 10958