Kovalevsky, A. A.; Nicolosi, F. On conditions of the nonexistence of solutions of nonlinear equations with data from classes close to \(L^1\). (English) Zbl 1289.35075 J. Partial Differ. Equations 26, No. 1, 39-47 (2013). Summary: We establish conditions of the nonexistence of weak solutions of the Dirichlet problem for nonlinear elliptic equations of arbitrary even order with some right-hand sides from \(L^m\) where \(m>1\). The conditions include the requirement of a certain closeness of the parameter \(m\) to 1. MSC: 35J25 Boundary value problems for second-order elliptic equations 35J40 Boundary value problems for higher-order elliptic equations 35J60 Nonlinear elliptic equations 35D30 Weak solutions to PDEs Keywords:nonlinear elliptic equations in divergence form; Dirichlet problem; weak solution; existence and nonexistence PDFBibTeX XMLCite \textit{A. A. Kovalevsky} and \textit{F. Nicolosi}, J. Partial Differ. Equations 26, No. 1, 39--47 (2013; Zbl 1289.35075) Full Text: DOI