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- W2003148613 abstract "Given a smooth Riemannian manifold (M,g) we investigate the existence of positive solutions to the equation−ε2Δgu+u=up−1on M which concentrate at some submanifold of M as ε→0, for supercritical nonlinearities. We obtain a positive answer for some manifolds, which include warped products. Using one of the projections of the warped product or some harmonic morphism, we reduce this problem to a problem of the form−ε2divh(c(x)∇hu)+a(x)u=b(x)up−1, with the same exponent p, on a Riemannian manifold (M,h) of smaller dimension, so that p turns out to be subcritical for this last problem. Then, applying Lyapunov–Schmidt reduction, we establish existence of a solution to the last problem which concentrates at a point as ε→0." @default.
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- W2003148613 date "2014-12-01" @default.
- W2003148613 modified "2023-10-03" @default.
- W2003148613 title "Solutions to a singularly perturbed supercritical elliptic equation on a Riemannian manifold concentrating at a submanifold" @default.
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- W2003148613 doi "https://doi.org/10.1016/j.jmaa.2014.05.079" @default.
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