On the Number of Radially Symmetric Solutions to Dirichlet Problems with Jumping Nonlinearities of Superlinear Order

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
Hendrik J. Kuiper, Arizona State University

Document Type

Article

Department

Mathematics (HMC)

Publication Date

1-1999

Abstract

This paper is concerned with the multiplicity of radially symmetric solutions u(x) to the Dirichlet problem

Δu+f(u)=h(x)+cφ(x)

on the unit ball Ω⊂R^N with boundary condition u=0 on ∂Ω. Here φ(x) is a positive function and f(u) is a function that is superlinear (but of subcritical growth) for large positive u, while for large negative u we have that f'(u)<μ, where μ is the smallest positive eigenvalue for Δψ+μψ=0 in Ω with ψ=0 on ∂Ω. It is shown that, given any integer k≥0, the value c may be chosen so large that there are 2k+1 solutions with k or less interior nodes. Existence of positive solutions is excluded for large enough values of c.

Comments

First published in Transactions of the American Mathematical Society in Vol 351-5(1999), published by the American Mathematical Society

Rights Information

© 1999 American Mathematical Society

DOI

10.1090/S0002-9947-99-02110-8

Recommended Citation

Castro, Alfonso and Kuiper, Hendrik J., "On the Number of Radially Symmetric Solutions to Dirichlet Problems with Jumping Nonlinearities of Superlinear Order" (1999). All HMC Faculty Publications and Research. 471.
https://scholarship.claremont.edu/hmc_fac_pub/471