On the existence of sulutions of the equation Lx ∞ Nx and a coincidence degree theory

Abstract

The coincidence degree for the pair (L, N) developed by Mawhin (1972) provides a method for proving the existence of solutions of the equation Lx = Nx where L: dom L ⊂ X → Z is a linear Fredholm mapping of index zero and is a (possiblv nonlinear) mapping and Ω is a bounded open subset of X, X and Z being normed linear spaces over the reals. In this paper we have extended the coincidence degree for the pair (L, N) to solve the equation , where L: dom L ⊂ X → Z is a linear Fredholm mapping of index zero, and X, Z and Ω are as above, CK(Z) being the set of compact convex subsets of Z.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 47 H 15, 47 A 50; secondary 47 H 10, 47 A 55.