Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Radially symmetric solutions to a superlinear Dirichlet problem in a ball with jumping nonlinearities
HTML articles powered by AMS MathViewer

by Alfonso Castro and Alexandra Kurepa PDF
Trans. Amer. Math. Soc. 315 (1989), 353-372 Request permission

Abstract:

Let $p,\varphi :[0,T] \to R$ be bounded functions with $\varphi > 0$. Let $g:{\mathbf {R}} \to {\mathbf {R}}$ be a locally Lipschitzian function satisfying the superlinear jumping condition: (i) ${\lim _{u \to - \infty }}(g(u)/u) \in {\mathbf {R}}$ (ii) ${\lim _{u \to \infty }}(g(u)/{u^{1 + \rho }}) = \infty$ for some $\rho > 0$, and (iii) ${\lim _{u \to \infty }}{(u/g(u))^{N/2}}(NG(\kappa u) - ((N - 2)/2)u \cdot g(u)) = \infty$ for some $\kappa \in (0,1]$ where $G$ is the primitive of $g$. Here we prove that the number of solutions of the boundary value problem $\Delta u + g(u) = p(\left \| x\right \|) + c\varphi (\left \| x\right \|)$ for $x \in {{\mathbf {R}}^N}$ with $\left \| x\right \| < T,u(x) = 0$ for $\left \| x\right \| = T$ tends to $+ \infty$ when $c$ tends to $+ \infty$. The proofs are based on the "energy" and "phase plane" analysis.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 35J65, 35B05
  • Retrieve articles in all journals with MSC: 35J65, 35B05
Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 315 (1989), 353-372
  • MSC: Primary 35J65; Secondary 35B05
  • DOI: https://doi.org/10.1090/S0002-9947-1989-0933323-8
  • MathSciNet review: 933323