Entire Large Solutions for Competitive Semilinear Elliptic Systems with General Nonlinearities Satisfying Keller--Osserman Conditions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917095111917568 |
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| author | Covei, Dragos-Patru |
| author_facet | Covei, Dragos-Patru |
| contents | We generalize a theorem of Lair concerning the existence of positive entire large solutions to competitive semilinear elliptic systems. While Lair's original result \cite{Lair2025} was established for power-type nonlinearities, our work extends the theory to a broad class of general nonlinearities satisfying a Keller--Osserman-type growth condition. The proof follows the same conceptual framework monotone iteration to construct global positive solutions, reduction to a scalar inequality for the sum of the components, application of a Keller--Osserman transform, and a two-step radial integration argument but replaces the explicit power-law growth with a general monotone envelope function. This approach yields a unified and verifiable criterion for the existence of large solutions in terms of the Keller--Osserman integral, thereby encompassing both critical and supercritical growth regimes within a single analytical setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_11933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entire Large Solutions for Competitive Semilinear Elliptic Systems with General Nonlinearities Satisfying Keller--Osserman Conditions Covei, Dragos-Patru Analysis of PDEs We generalize a theorem of Lair concerning the existence of positive entire large solutions to competitive semilinear elliptic systems. While Lair's original result \cite{Lair2025} was established for power-type nonlinearities, our work extends the theory to a broad class of general nonlinearities satisfying a Keller--Osserman-type growth condition. The proof follows the same conceptual framework monotone iteration to construct global positive solutions, reduction to a scalar inequality for the sum of the components, application of a Keller--Osserman transform, and a two-step radial integration argument but replaces the explicit power-law growth with a general monotone envelope function. This approach yields a unified and verifiable criterion for the existence of large solutions in terms of the Keller--Osserman integral, thereby encompassing both critical and supercritical growth regimes within a single analytical setting. |
| title | Entire Large Solutions for Competitive Semilinear Elliptic Systems with General Nonlinearities Satisfying Keller--Osserman Conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.11933 |