Radial Symmetry of Positive Solutions of Nonlinear Elliptic Equations Academic Article uri icon

abstract

  • We study the radial symmetry and asymptotic behavior at x=∞ of positive solutions of Δu=φ(single rule fence sign x single rule fence sign) uλ,x∈Rn and single rule fence sign x single rule fence sign large where λ1 and φ(r) is positive and continuous for r large. In particular we give conditions on φ which guarantee that each positive solution of (*) satisfies u(x)ū(single rule fence sign x) single rule fence sign →1as single rule fence sign x single rule fence sign →∞ where ū(r) is the average of u on the sphere single rule fence sign x single rule fence sign=r. © 1999 Academic Press.

author list (cited authors)

  • Taliaferro, S. D.

citation count

  • 1

publication date

  • August 1999