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Infinite multiplicity for an inhomogeneous supercritical problem in entire space


Authors: Baishun Lai and Zhihao Ge
Journal: Proc. Amer. Math. Soc. 139 (2011), 4409-4418
MSC (2000): Primary 35J25, 35J20
Published electronically: April 27, 2011
MathSciNet review: 2823086
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Abstract: In this paper, we will prove the existence of infinitely many positive solutions to the following supercritical problem by using the Liapunov-Schmidt reduction method and asymptotic analysis:

\begin{displaymath}\left\{ \begin{array}{ll} \Delta u + u^{p}+f(x)=0, \ u>0 \ \m... ...},\\ \lim_{\vert x\vert\to\infty}u(x)\to 0. \end{array}\right.\end{displaymath}      


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Additional Information

Baishun Lai
Affiliation: Institute of Contemporary Mathematics, Henan University, Kaifeng 475004, People’s Republic of China
Address at time of publication: School of Mathematics and Information Science, Henan University, Kaifeng 475004, People’s Republic of China
Email: laibaishun@henu.edu.cn

Zhihao Ge
Affiliation: School of Mathematics and Information Science, Henan University, Kaifeng 475004, People’s Republic of China
Email: zhihaoge@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2011-10902-X
Keywords: Critical exponents, linearized operators, supercritical problem.
Received by editor(s): October 21, 2010
Published electronically: April 27, 2011
Additional Notes: The first author was supported in part by National Natural Science Foundation of China Grant 10971061 and Natural Science Foundation of Henan Province Grant 112300410054.
The second author was supported in part by National Natural Science Foundation of China Grant 10901047
Communicated by: Walter Craig
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.