Abstract.
We study the radially symmetric Schrödinger equation
with N ≥ 1, ɛ > 0 and p > 1. As ɛ→ 0, we prove the existence of positive radially symmetric solutions concentrating simultaneously on k spheres. The radii are localized near non-degenerate critical points of the function \(\Gamma (r) = r^{{N - 1}} {\left[ {V(r)} \right]}^{{\frac{{p + 1}}{{p - 1}} - \frac{1}{2}}} {\left[ {W(r)} \right]}^{{ - \frac{2} {{p - 1}}}}. \)
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Supported by the Alexander von Humboldt foundation in Germany and NSFC (No:10571069) in China.
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Bartsch, T., Peng, S. Semiclassical symmetric Schrödinger equations: Existence of solutions concentrating simultaneously on several spheres. Z. angew. Math. Phys. 58, 778–804 (2007). https://doi.org/10.1007/s00033-006-5111-x
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DOI: https://doi.org/10.1007/s00033-006-5111-x