The existence and uniqueness of bound-state solutions of a semi-linear equation
| Autor: | Troy, W.C |
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| Zdroj: | Proceedings A: Mathematical, Physical and Engineering Sciences; September 2005, Vol. 461 Issue: 2061 p2941-2963, 23p |
| Abstrakt: | We investigate the existence and uniqueness of bounded, radially symmetric solutions in R3of Δuf(u)0, where f(u) is continuous, piecewise linear, and has three distinct real zeros. We give a detailed construction of the first two bound states which satisfy as r→∞. The first is the well known positive bound-state solution. The second solution changes sign and has exactly one zero in (0,∞). We prove that both of these solutions are unique. |
| Databáze: | Supplemental Index |
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