In this paper we generalize and improve some well-known solvability conditions for semilinear elliptic boundary value problems at resonance within the context of Besov and Triebel-Lizorkin spaces. In particular we will show that many such solvability conditions can be viewed as special cases of a single generalized Landesman-Lazer condition. Our methods apply an adaptation of Leray-Schauder degree ideas to quasi-Banach spaces.
"Solvability conditions for semilinear elliptic boundary value problems at resonance with bounded and unbounded nonlinear terms." Adv. Differential Equations 3 (4) 595 - 624, 1998.