Non-singular solutions of two-point problems, with multiple changes of sign in the nonlinearity
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- by Philip Korman
- Proc. Amer. Math. Soc. 144 (2016), 2539-2546
- DOI: https://doi.org/10.1090/proc/12905
- Published electronically: October 22, 2015
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Abstract:
We prove that positive solutions of the two-point boundary value problem \[ u''(x)+\lambda f(u(x))=0,\;\; \mbox {for $-1<x<1$},\;\; u(-1)=u(1)=0,\] satisfying $\max u=u(0)>\gamma$, are non-singular, provided that $f(u)$ is predominantly negative for $u \in (0,\gamma ]$, and superlinear for $u>\gamma$. This result adds a solution curve without turns to whatever is known about the solution set for $u(0) \in (0,\gamma )$. In particular, we combine it with the well-known cases of parabola-like, or $S$-shaped solution curves.References
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Bibliographic Information
- Philip Korman
- Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025
- MR Author ID: 200737
- Email: kormanp@ucmail.uc.edu
- Received by editor(s): October 27, 2014
- Received by editor(s) in revised form: July 14, 2015
- Published electronically: October 22, 2015
- Communicated by: Joachim Krieger
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2539-2546
- MSC (2010): Primary 34B15
- DOI: https://doi.org/10.1090/proc/12905
- MathSciNet review: 3477070