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On conditions of the nonexistence of solutions of nonlinear equations with data from classes close to \(L^1\). (English) Zbl 1289.35075

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
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