Abstract
This paper is concerned with multiplicity results for semilinear elliptic equations of the type \(-\Delta u+a(x)u=\left| u\right| ^{p-2}u+f\left( x,u\right) \) in \(\Omega \), \(u=0\) on \(\partial \Omega \). We obtain at least two nontrivial solutions for this type of equations with the case that 0 is not a local minimizer of the corresponding functional under suitable hypotheses. The method we used here is based on a linking structure relevant to the Nehari manifold.
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Acknowledgements
We are grateful to the referees for perusing this manuscript and giving valuable suggestions. Moreover, the first author would like to appreciate for strong supports by NSFC (11471319) and BCMIIS (Beijing Center for Mathematics and Information Interdisciplinary Sciences).
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Communicated by P. Rabinowitz.
Chong Li is supported by NSFC (11471319) and BCMIIS.
Yanyan Liu is supported by NSFC (11471319).
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Li, C., Liu, Y. Multiple solutions for a class of semilinear elliptic problems via Nehari-type linking theorem. Calc. Var. 56, 20 (2017). https://doi.org/10.1007/s00526-017-1111-2
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DOI: https://doi.org/10.1007/s00526-017-1111-2