Uniqueness and nonuniqueness for positive radial solutions of \(\Delta u+f(u,r)=0\). (English) Zbl 0581.35021
The authors give existence and nonexistence results for radial solutions of the equation \(\Delta u+f(u,| x|)=0\).
Reviewer: M.Biroli
MSC:
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35A05 | General existence and uniqueness theorems (PDE) (MSC2000) |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
References:
| [1] | Ambrosetti, J. Funct. Anal. 14 pp 349– (1973) |
| [2] | Berryman, Arch. Rational Mech. Anal. 74 pp 379– (1980) |
| [3] | Brezis, Comm. Pure Appl. Math. 36 pp 437– (1983) |
| [4] | An introduction to the Study of Stellar Structure, University of Chicago Press, 1939. |
| [5] | Coffman, J. Diff. Eqns. 3 pp 92– (1967) |
| [6] | Coffman, Arch. Rational Mech. Anal. 46 pp 81– (1972) |
| [7] | A nonlinear boundary value problem with many positive solutions, Preprint. |
| [8] | Caffarelli, Duke Math. J. 47 pp 705– (1980) |
| [9] | DeFigueiredo, J. Math. Pures Appl. 61 pp 41– (1982) |
| [10] | Gidas, Comm. Math. Phys. 68 pp 209– (1979) |
| [11] | Hempel, Indiana Univ. Math. J. 26 pp 265– (1977) |
| [12] | Henon, Astron. and Astrophys. 24 pp 229– (1973) |
| [13] | Kazdan, Comm. Pure Appl. Math. 28 pp 567– (1975) |
| [14] | Kolodner, Comm. Pure Appl. Math. 8 pp 395– (1955) |
| [15] | McLeod, Proc. Natl. Acad. Sci. U.S.A. 78 pp 6592– (1981) |
| [16] | Nehari, Trans. Amer. Math. Soc. 95 pp 101– (1960) |
| [17] | Ni, J. Diff. Equs. 50 (1983) |
| [18] | Ni, Indiana Univ. Math. J. 31 pp 801– (1982) |
| [19] | Ni, Trans. Amer. Math. Soc. |
| [20] | Nussbaum, J. Math. Anal. Appl. 51 pp 461– (1975) |
| [21] | Rabinowitz, Indiana Univ. Math. J. 23 pp 729– (1974) |
| [22] | An example for the plasma problem with infinitely many solutions, preprint (unpublished), 1978. |
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