Multi-bump solutions to Carrier's problem |
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Authors: | Shangbing Ai |
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Institution: | School of Mathematics (CDSNS), Georgia Institute of Technology, Atlanta, GA 30332-0160, USA |
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Abstract: | 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|lnε|), while only single spikes are allowed near the boundaries x=±1. |
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Keywords: | Multi-spike solutions Shooting argument Singular perturbation |
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