On Conditions of the Nonexistence of Solutions of Nonlinear Equations with Data from Classes Close to <em>L</em>¹

Abstract

Abstract. We establish conditions of the nonexistence of weak solutions of the Dirichlet problem for nonlinear elliptic equations of arbitrary even order with some righthand sides from L m where m > 1. The conditions include the requirement of a certain closeness of the parameter m to 1. AMS Subject Classifications: 35J25, 35J40, 35J60Chinese Library Classifications: O175.8, O175.25, O175.29Key Words: Nonlinear elliptic equations in divergence form; Dirichlet problem; weak solution; existence and nonexistence of weak solutions.