RADIAL SYMMETRY OF POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS IN $R^n$

  • Naito, Yuki (Department of Applied Mathematics Faculty of Engineering Kobe University)
  • Published : 2000.09.01

Abstract

Symmetry properties of positive solutions for semilinear elliptic problems in n are considered. We give a symmetry result for the problem in the feneral case, and then derive various results for certain classes of demilinear elliptic equations. We employ the moving plane method based on the maximum principle on unbounded domains to obtain the result on symmetry.

Keywords

References

  1. Nonlinear Analysis T. M. A. v.28 On the solution structures of the semilinear elliptic equations on $R^n$ J. -L. Chern
  2. Comm. Math. Phys. v.68 Symmetry and related properties via the maximum principle B. Gidas;W. -M. Ni;L. Nirenberg
  3. in Mathematical Analysis and Applications v.7 Symmetry of positive solutions of nonlinear elliptic equations in $R^n$
  4. Amer. J. Math. v.106 On exterior Direchlet problem with applications to some nonlinear equations arising in geometry C. E. Kenig;W. -M. Ni
  5. Comm. Partial Differential Equations v.16 Monotonicity and symmetry of fully nonlinear elliptic equations on unbounded domains C. Li
  6. Duke Math. J. v.70 On the positive solutions of the Matukuma equation Y. Li
  7. Arch. Rational Mech. Anal. v.108 On the existence and symmetry properties of finite total mass solutions of the Matukuma equation, the Eddington equation and their generalizations Y. Li;W. -M. Ni
  8. Arch. Rational Mech. Anal. v.118 On the asymptotic behavior and radial symmetry of positive solutions of semilinar elliptic equations in $R^n$
  9. Comm. Partial DIfferential Equations v.18 Radial symmetry of positive solutions of nonlinear elliptic equations in $R^n$
  10. Proc. Amer. Math. Soc. v.95 On the elliptic equation $D_j$[$a_ij$(x)$D_3$U] - k(x)U + K(x)$U^p$ = 0 F. -H. Lin
  11. Differential Integral Equations v.11 A note on radial symmetry of positive solutions for semilinear elliptic equations in $R^n$ Y. Naito
  12. Maximum Principles in Differential Equations M. Protter;H. Weinberger
  13. Arch. Rational Mech. Anal. v.43 A symmetry problem in potential theory J. Serrin
  14. J. Differential Equations v.120 Symmetry of positive solutions of △u + $u^p$ = 0 in $R^n$ H. Zou
  15. Indiana Univ. Math. J. v.45 Symmetry of ground states of semilinear elliptic equations with mixed Sobolev growth