General existence theorems for quasilinear elliptic systems without monotonicity
Existence theorems for quasilinear elliptic systems \(Lu(x)=f(x,u(x))\) and \(Lu(x)=g(x,u(x),Vu(x)),\) subject to zero Dirichlet boundary conditions, are given, where L is a vector valued second order uniformly elliptic differential operator, and f and g are vector valued Carathéodory functions. The method builds on a priori estimates for the Leray-Schauder continuation principle, the general theory of superposition operators in ideal function spaces, and recent results on Orlicz spaces of vector- valued functions.
second order quasilinear elliptic systems
scientific article; zbMATH DE number 4127697
scientific article