Radially Symmetric Solutions to a Superlinear Dirichlet Problem in a Ball with Jumping Nonlinearities

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
Alexandra Kurepa, Texas Christian UniversityFollow

Document Type

Article

Department

Mathematics (HMC)

Publication Date

9-1989

Abstract

Let p,φ :[0,T] → R be bounded functions with φ > 0. Let g:R → R be a locally Lipschitzian function satisfying the superlinear jumping condition:

(i) lim u → - ∞ (g(u)/u) ε R

(ii) lim u → ∞ (g(u)/(u^{1 + ρ} )) = ∞ for some ρ > 0, and

(iii) lim u → ∞ (u/g(u))^N/2(NG(κ u) - ((N - 2)/2)u · g(u)) = ∞ for some κ ε (0,1] where G is the primitive of g.

Here we prove that the number of solutions of the boundary value problem Δu + g(u) = p(|x|) + cφ (|x|) for x ε R^N with |x| < T, u(x) = 0 for |x| = T$ tends to +∞ when c tends to +∞. The proofs are based on the "energy" and "phase plane" analysis.

Comments

First published in Transactions of the American Mathematical Society in Vol 315-1(1989), published by the American Mathematical Society

Rights Information

© 1989 American Mathematical Society

DOI

10.1090/S0002-9947-1989-0933323-8

Recommended Citation

Castro, Alfonso and Kurepa, Alexandra, "Radially Symmetric Solutions to a Superlinear Dirichlet Problem in a Ball with Jumping Nonlinearities" (1989). All HMC Faculty Publications and Research. 465.
https://scholarship.claremont.edu/hmc_fac_pub/465