Nonselfadjoint semilinear elliptic boundary value problems
The author considers a semilinear elliptic boundary value problem \[ Au=g(x,Du)\quad on\quad \Omega,\quad Bu=0\quad on\quad \partial \Omega \] of order m at resonance, where g is bounded and Du denotes the vector of partial derivatives up to order m-1. The main new feature compared with earlier papers of \textit{H. Shaw} [J. Differ. Equations 26, 335-346 (1977; Zbl 0341.35039)] and the reviewer [ibid. 32, 186-192 (1979; Zbl 0377.35028)] is that no variable in Du is distinguished here, whereas before the main weight has been put on u. The abstract setting applies also to weakly coupled elliptic systems as indicated by examples. Its proof relies on the Leray-Schauder degree.
scientific article; zbMATH DE number 4103577