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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.09917 |
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| _version_ | 1866913690787250176 |
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| author | Wang, Mingxin Zhang, Lei |
| author_facet | Wang, Mingxin Zhang, Lei |
| contents | It is well known that, in the study of the dynamical properties of nonlinear evolution system with nonlocal dispersals, the principal eigenvalue of linearized system play an important role. However, due to lack of compactness, in order to obtain the existence of principal eigenvalue, certain additional conditions must be attached to the coefficients. In this paper, we approximate the generalized principal eigenvalue of nonlocal dispersal cooperative and irreducible system, which admits the Collatz-Wielandt characterization, by constructing the monotonic upper and lower control systems with principal eigenvalues; and show that the generalized principal eigenvalue plays the same role as the usual principal eigenvalue. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation of the generalized principal eigenvalue of cooperative nonlocal dispersal systems and applications Wang, Mingxin Zhang, Lei Classical Analysis and ODEs 35R20, 45C05, 45G15, 92D30 It is well known that, in the study of the dynamical properties of nonlinear evolution system with nonlocal dispersals, the principal eigenvalue of linearized system play an important role. However, due to lack of compactness, in order to obtain the existence of principal eigenvalue, certain additional conditions must be attached to the coefficients. In this paper, we approximate the generalized principal eigenvalue of nonlocal dispersal cooperative and irreducible system, which admits the Collatz-Wielandt characterization, by constructing the monotonic upper and lower control systems with principal eigenvalues; and show that the generalized principal eigenvalue plays the same role as the usual principal eigenvalue. |
| title | Approximation of the generalized principal eigenvalue of cooperative nonlocal dispersal systems and applications |
| topic | Classical Analysis and ODEs 35R20, 45C05, 45G15, 92D30 |
| url | https://arxiv.org/abs/2502.09917 |