On boundary value problems for partial differential equations of the form ℒ⁺ A(u,ℒu) = f

Abstract

Generalizedly posed boundary value problems for equations of the types ℒ⁺ Aℒu = f and ℒ⁺A(u, ℒ u) = f, where ℒ is some general differential operation with smooth matrix coefficients in a general bounded domain Ω and A(∙, ∙) is some continuous operator in the vector spaces L₂(Ω), are introdused and studied.