An Abstract Existence Theorem at Resonance and Its Applications,

By using Brouwer degree theory and a continuation theorem based on Mawhinʹs coincidence degree, an abstract existence theorem at resonance for operator equations is developed. As applications of this result, some sufficient conditions are given for the existence of periodic solutions of semilinear equations at resonance where the kernel of the linear part has dimensionN(N 2). The results due to Nagle and Sinkala are generalized, improved, and unified.