Find out how to access previewonly content
Semilinear elliptic equations of Matukumatype and related topics
 WeiMing Ni,
 Shoji Yotsutani
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
We investigate the structure of solutions of some semilinear elliptic equations, which include Matukuma’s equation as a special case. It is a mathematical model proposed by Matukuma, an astrophysicist, in 1930 to describe the dynamics of a globular cluster of stars. Equations of this kind have come up both in geometry and in physics, and have been a subject of extensive studies for some time. However, almost all the methods previously developed do not seem to apply to the original Matukuma’s equation. Our results cover most of the cases left open by previous works.
 H. Berestycki, P. L. Lions and L. A. Peletier, An ODE approach to the existence of positive soluions for semilinear problems inR ^{n}. Indiana Univ. Math. J.,30, (1981), 141–157. CrossRef
 S. Chandrasekhar, An Introduction to the Study of Stellar Structure. Univ. Chicago Press, 1939.
 W.Y. Ding and W.M. Ni, On the elliptic equation Δu+Ku ^{(n+2)/(n−2)}=0 and related topics. Duke Math. J.,52, (1985), 485–506. CrossRef
 W.Y. Ding and W.M. Ni, On the existence of positive entire solution of a semilinear elliptic equations. Arch. Rational Mech. Anal.,91, (1986), 283–308. CrossRef
 A. S. Eddington, The dynamics of a globular stellar system. Monthly Notices Royal Astronom. Soc.,75, (1915), 366–376.
 R. H. Fowler, Further studies of Emden’s and similar differential equations. Quart. J. Math. (Oxford Ser.),2 (1931), 259–287. CrossRef
 M. Hénon, Numerical experiments on the stability of spherical stellar systems. Astronom. and Astrophys.,24, (1973), 229–238.
 D. D. Joseph and T. S. Lundgren, Quasilinear Dirichlet problems driven by positive sources. Arch Rational Mech. Anal.,49, (1973), 241–269.
 N. Kawano, On bounded entire solutions of semilinear elliptic equations. Hiroshima Math. J.,14 (1984), 125–158.
 N. Kawano, J. Satsuma and S. Yotsutani, On the positive solutions of an Emdentype elliptic equation. Proc. Japan Acad. Ser. A,61, (1985), 181–189. CrossRef
 N. Kawano, J. Satsuma and S. Yotsutani, Existence of positive entire solutions of an Emdentype elliptic equation. Funkcial. Ekvac., to appear.
 T. Kusano and M. Naito, Oscillation theory of entire solutions of second order superlinear elliptic equations. Funkcial. Ekvac., to appear.
 T. Matukuma, Dynamics of globular clusters. Nippon Temmongakkai Yoho,1, (1930), 68–89 (In Japanese).
 T. Matukuma, Sur la dynamique des amas globulaires stellaires. Proc. Imp. Acad.,6, (1930), 133–136. CrossRef
 T. Matukuma, The Cosmos. Iwanami Shoten, Tokyo, 1938 (In Japanese).
 K. McLeod and J. Serrin, Uniquenss of solutions of semilinear Poisson equations. Proc. Nat. Acad. Sci. USA.,78, (1981), 6592–6595. CrossRef
 R. McOwen, Conformal metrics inR ^{2} with prescribed Gaussian curvature and positive total curvature. Indiana Univ. Math. J.,34, (1985), 97–104. CrossRef
 M. Naito, A note on bounded positive entire solution of semiliner elliptic equations. Hiroshima Math. J.,14, (1984), 211–214.
 W.M. Ni, On the elliptic equation Δu+K(x)u ^{(n+2)/(n−2)}=0 its generalization, and applications in geometry. Indiana Univ. Math. J.,31, (1982), 493–529. CrossRef
 W.M. Ni, On the positive radial solutions of some semilinear elliptic equations onR ^{ n }. Appl. Math. Optim.,9, (1983), 373–380. CrossRef
 W.M. Ni, Uniqueness, nonuniqueness and related questions of nonlinear elliptic and parabolic equations. Proc. Symp. Pure Math., 45, Amer. Math. Soc., 1986, 229–241.
 W.M. Ni and R. D. Nussbaum, Uniqueness and nonuniqueness for positive radial solutions of Δu+f(u,r)=0. Comm. Pure Appl. Math.,38, (1985), 67–108. CrossRef
 W.M. Ni and J. Serrin, Existence and nonexistence theorems for ground states for quasilinear partial differential equations. Accad. Naz. dei Lincei,77, (1986), 231–257.
 W.M. Ni and S. Yotsutani, On the Matukuma’s equation and related topics. Proc. Japan Acad. Ser. A,62, (1986), 260–263. CrossRef
 N. Kawano, W.M. Ni and S. Yotsutani, In preparation.
 Title
 Semilinear elliptic equations of Matukumatype and related topics
 Journal

Japan Journal of Applied Mathematics
Volume 5, Issue 1 , pp 132
 Cover Date
 19880201
 DOI
 10.1007/BF03167899
 Print ISSN
 09102043
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 semilinear
 elliptic equations
 astrophysics
 Authors

 WeiMing Ni ^{(1)}
 Shoji Yotsutani ^{(2)}
 Author Affiliations

 1. School of Mathematics, University of Minnesota, 55455, Minneapolis, Minnesota, U.S.A.
 2. Department of Applied Science, Miyazaki University, 88921, Miyazaki, Japan