Exponential decay of solutions to nonlinear elliptic equations with potentials |
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Authors: | Reika Fukuizumi Tohru Ozawa |
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Institution: | (1) Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan |
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Abstract: | Exponential decay estimates are obtained for complex-valued solutions to nonlinear elliptic equations in
where the linear term is given by Schr?dinger operators H = − Δ + V with nonnegative potentials V and the nonlinear term is given by a single power with subcritical Sobolev exponent in the attractive case. We describe specific
rates of decay in terms of V, some of which are shown to be optimal. Moreover, our estimates provide a unified understanding of two distinct cases in
the available literature, namely, the vanishing potential case V = 0 and the harmonic potential case V(x) = |x|2.
Dedicated to Professor Jun Uchiyama on the occasion of his sixtieth birthday
Received: May 4, 2004 |
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Keywords: | 35J60 35B40 |
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