Existence and large radial solutions for an elliptic system under finite new Keller-Osserman integral conditions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915630533312512 |
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| author | Covei, Dragos-Patru |
| author_facet | Covei, Dragos-Patru |
| contents | We study the semilinear elliptic system
\[ Δu = p(|x|)\,g(v), \qquad Δv = q(|x|)\,f(u), \qquad x \in \mathbb{R}^n,\; n \geq 3, \]
under new Keller--Osserman-type integral conditions on the nonlinearities $f,g$ and decay constraints on the radial weights $p,q$. Within this framework we prove: (i) existence of infinitely many entire positive radial solutions for admissible central values; (ii) closedness of the set of all admissible central values; and (iii) largeness (blow-up at infinity) of solutions at boundary points. The analysis combines comparison principles, compactness arguments, and Keller--Osserman transforms, thereby extending classical theory to coupled elliptic systems with general nonlinearities and weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and large radial solutions for an elliptic system under finite new Keller-Osserman integral conditions Covei, Dragos-Patru Analysis of PDEs We study the semilinear elliptic system \[ Δu = p(|x|)\,g(v), \qquad Δv = q(|x|)\,f(u), \qquad x \in \mathbb{R}^n,\; n \geq 3, \] under new Keller--Osserman-type integral conditions on the nonlinearities $f,g$ and decay constraints on the radial weights $p,q$. Within this framework we prove: (i) existence of infinitely many entire positive radial solutions for admissible central values; (ii) closedness of the set of all admissible central values; and (iii) largeness (blow-up at infinity) of solutions at boundary points. The analysis combines comparison principles, compactness arguments, and Keller--Osserman transforms, thereby extending classical theory to coupled elliptic systems with general nonlinearities and weights. |
| title | Existence and large radial solutions for an elliptic system under finite new Keller-Osserman integral conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.04099 |