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In this paper, we obtain the existence of weak solutions to a class of strongly anisotropic nonlinear elliptic boundary-value problems with nonlinear lower-order term with natural growth in an appropriate anisotropic function space. We investigate the cases where the right hand side term is regular or to be in . A uniqueness result is also given in a particular case.
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Moussa Chrif, Said El Manouni, Fares Mokhtari, Strongly anisotropic elliptic problems with regular and data. Port. Math. 72 (2015), no. 4, pp. 357–391DOI 10.4171/PM/1971