Radially Symmetric Solutions to a Dirichlet Problem Involving Critical Exponents

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
Alexandra Kurepa, North Carolina A & T State UniversityFollow

Document Type

Article

Department

Mathematics (HMC)

Publication Date

6-1994

Abstract

In this paper we answer, for N = 3,4, the question raised in [1] on the number of radially symmetric solutions to the boundary value problem -Δu(x) = λu(x) + u(x)|u(x)|^{4/(N-2)}, x ε B: = x ε R^N:{|x| < 1}, u(x)=0, x ε ∂B, where Δ is the Laplacean operator and λ>0. Indeed, we prove that if N = 3,4, then for any λ>0 this problem has only finitely many radial solutions. For N = 3,4,5 we show that, for each λ>0, the set of radially symmetric solutions is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.

Comments

First published in Transactions of the American Mathematical Society in Vol 343-2(1994), published by the American Mathematical Society

Rights Information

© 1994 American Mathematical Society

DOI

10.1090/S0002-9947-1994-1207581-0

Recommended Citation

Castro, Alfonso and Kurepa, Alexandra, "Radially Symmetric Solutions to a Dirichlet Problem Involving Critical Exponents" (1994). All HMC Faculty Publications and Research. 466.
https://scholarship.claremont.edu/hmc_fac_pub/466