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A numerical approach to the proof of existence of solutions for elliptic problems
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inferred← citeshttps://doi.org/10.1002/zamm.19940741210openalex-snapshot
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inferred← citeshttps://doi.org/10.1006/jmaa.1997.5712openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.jde.2015.12.041openalex-snapshot
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inferred← citeshttps://doi.org/10.1080/01630563.2012.677918openalex-snapshot
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inferred← citeshttps://doi.org/10.1080/01630569108816449openalex-snapshot
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inferred← citeshttps://doi.org/10.1080/01630569908816910openalex-snapshot
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inferred← citeshttps://doi.org/10.1081/nfa-100105107openalex-snapshot
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inferred← citeshttps://doi.org/10.1088/1361-6544/ade5e5openalex-snapshot
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inferred← citeshttps://doi.org/10.1109/iscas.1992.230623openalex-snapshot
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inferred← citeshttps://doi.org/10.1137/s0036142996304498openalex-snapshot
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inferred← citeshttps://doi.org/10.11606/t.55.2020.tde-04022020-113120openalex-snapshot
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inferred← citeshttps://doi.org/10.12921/cmst.2019.0000016openalex-snapshot
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inferred← citeshttps://doi.org/10.14492/hokmj/1272848033openalex-snapshot
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inferred← citeshttps://doi.org/10.15248/proc.2.441openalex-snapshot
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inferred← citeshttps://doi.org/10.1587/essfr.2.3_19openalex-snapshot
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inferred← citeshttps://doi.org/10.1587/nolta.1.105openalex-snapshot
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inferred← citeshttps://doi.org/10.1587/nolta.2.111openalex-snapshot
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inferred← citeshttps://doi.org/10.1587/nolta.4.34openalex-snapshot
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inferred← citeshttps://doi.org/10.1587/nolta.5.320openalex-snapshot
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inferred← citeshttps://doi.org/10.2478/fcds-2013-0009openalex-snapshot
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inferred← citeshttps://doi.org/10.3850/978-981-08-5118-7_054openalex-snapshot
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inferred← citeshttps://doi.org/10.48550/arxiv.1408.4678openalex-snapshot
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inferred← citeshttps://doi.org/10.48550/arxiv.1606.03818openalex-snapshot
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inferred← citeshttps://doi.org/10.5109/13475openalex-snapshot
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inferred← citeshttps://doi.org/10.5772/intechopen.101357openalex-snapshot
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