Uniqueness of positive radial solutions for a class of infinite semipositone $p$-Laplacian problems in a ball
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- by K. D. Chu, D. D. Hai and R. Shivaji PDF
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Abstract:
We prove uniqueness of positive radial solutions to the $p$-Laplacian problem \begin{equation*} \left \{ \begin {array}{c} -\Delta _{p}u=\lambda f(u)\text { in }\Omega , \\ u=0\text { on }\partial \Omega , \end{array} \right . \end{equation*} where $\Delta _{p}u=\operatorname {div}(|\nabla u|^{p-2}\nabla u),p\geq 2,\ \Omega$ is the open unit ball in $R^{N}, N>1,\ f:(0,\infty )\rightarrow \mathbb {R}$ is concave, $p$-sublinear at $\infty$ with infinite semipositone structure at $0$, and $\lambda$ is a large parameter.References
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Additional Information
- K. D. Chu
- Affiliation: Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
- Email: chuduckhanh@tdtu.edu.vn
- D. D. Hai
- Affiliation: Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
- MR Author ID: 243105
- Email: dang@math.msstate.edu
- R. Shivaji
- Affiliation: Department of Mathematics and Statisitics, University of North Carolina at Greensboro, Greensboro, North Carolina 27402
- MR Author ID: 160980
- Email: shivaji@uncg.edu
- Received by editor(s): June 25, 2019
- Received by editor(s) in revised form: September 12, 2019
- Published electronically: January 13, 2020
- Communicated by: Wenxian Shen
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 2059-2067
- MSC (2010): Primary 34B16; Secondary 34B18, 35J62
- DOI: https://doi.org/10.1090/proc/14886
- MathSciNet review: 4078089