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Positive solutions of semilinear elliptic equations with small perturbations


Author: Ryuji Kajikiya
Journal: Proc. Amer. Math. Soc. 141 (2013), 1335-1342
MSC (2010): Primary 35J20, 35J25, 35J60
DOI: https://doi.org/10.1090/S0002-9939-2012-11569-2
Published electronically: August 30, 2012
MathSciNet review: 3008880
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Abstract: In this paper, we study the semilinear elliptic equation with a small perturbation. We assume the main term in the equation to have a mountain pass structure but do not suppose any condition for the perturbation term. Then we prove the existence of a positive solution. Moreover, we prove the existence of at least two positive solutions if the perturbation term is nonnegative.


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Additional Information

Ryuji Kajikiya
Affiliation: Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502, Japan
Email: kajikiya@ms.saga-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2012-11569-2
Keywords: Mountain pass lemma, positive solution, perturbation problem, semilinear elliptic equation, variational method
Received by editor(s): August 18, 2011
Published electronically: August 30, 2012
Additional Notes: The author was supported in part by the Grant-in-Aid for Scientific Research (C) (No. 20540197), Japan Society for the Promotion of Science
Communicated by: Walter Craig
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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