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Variational approach to bifurcation from infinity for nonlinear elliptic problems

Published online by Cambridge University Press:  18 March 2013

Jaeyoung Byeon  and
Youngae Lee
Jaeyoung Byeon
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang, Kyungbuk 790-784, Republic of Korea (jbyeon@postech.ac.kr; duddofl@postech.ac.kr)
Youngae Lee
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang, Kyungbuk 790-784, Republic of Korea (jbyeon@postech.ac.kr; duddofl@postech.ac.kr)
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Abstract

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For any N ⩾ 1 and sufficiently small ε > 0, we find a positive solution of a nonlinear elliptic equation

when lim|x| → ∞V(x) = m > 0 and some optimal conditions on f are satisfied. Furthermore, we investigate the asymptotic behaviour of the solution as ε → 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 2 , April 2013 , pp. 269 - 301
Copyright
Copyright © Royal Society of Edinburgh 2013