Multi-bump solutions to Carrier’s problem

We study the existence of well-known singularly perturbed BVP problem ε2y = 1 − y2 − 2b(1 − x2)y, y(−1) = y(1) = 0 introduced by G.F. Carrier. In particular, we show that there exist multi-spike solutions, and the locations of interior spikes are clustered near x = 0 and are separated by an amount of O(ε|ln ε|), while only single spikes are allowed near the boundaries x =±1.  2003 Elsevier Science (USA). All rights reserved.