On the existence of sulutions of the equationLx∞Nxand a coincidence degree theory
E Tarafdar, Suat Khoh Teo · Journal of the Australian Mathematical Society · 1979
The coincidence degree for the pair (L, N) developed by Mawhin (1972) provides a method for proving the existence of solutions of the equationLx = NxwhereL: domL⊂X→Zis a linear Fredholm mapping of index zero and is a (possiblv nonlinear) mapping and Ω is a bounded open subset ofX, XandZbeing normed linear spaces over the reals. In this paper we have extended the coincidence degree for the pair (L, N) to solve the equation , whereL: domL⊂X→Zis a linear Fredholm mapping of index zero, andX, Zand Ω are as above,CK(Z)being the set of compact convex subsets ofZ. Subject classification (Amer. Math. Soc. (MOS) 1970): primary 47 H 15, 47 A 50; secondary 47 H 10, 47 A 55.