Abstract
For a bounded domain \(\Omega \), we establish existence and multiplicity of nontrivial solutions for the semilinear elliptic problem
where \(h\in L^\infty (\Omega )\) is nonnegative and nontrivial, g is asymptotically linear, f is superlinear and \({g(0)}=f(0)=0\). We also study the existence of solutions for the problem
when \(k\in L^2(\Omega )\).
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The authors wish to thank the anonymous reviewer for a careful reading of the paper and for all the suggestions.
Funding
This study was financed in part by FEDER-MINECO (Spain) grant PID2021-122122NB-I00 and “Junta de Andalucía” FQM-116. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
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D. Arcoya was supported by FEDER-MINECO (Spain) grant PID2021-122122NB-I00 and “Junta de Andalucía” FQM-116; F. O. de Paiva was supported by CAPES (Brazil)
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Arcoya, D., de Paiva, F.O. & Mendoza, J.M. Existence and multiplicity of solutions for a locally coercive elliptic equation. Partial Differ. Equ. Appl. 5, 9 (2024). https://doi.org/10.1007/s42985-024-00275-1
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DOI: https://doi.org/10.1007/s42985-024-00275-1