Positive radial solutions for a noncooperative resonant nuclear reactor model with sign-changing nonlinearities
Abstract This paper is concerned with the existence of positive radial solutions of the following resonant elliptic system: { − Δ u = u v + f ( | x | , u ) , 0 < R 1 < | x | < R 2 , x ∈ R N , − Δ v = c g ( u ) − d v , 0 < R 1 < | x | < R 2 , x ∈ R N , ∂ u ∂ n = 0 = ∂ v ∂ n , | x |...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02611-0 |
| _version_ | 1818590287305375744 |
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| author | Ruipeng Chen Jiayin Liu Guangchen Zhang Xiangyu Kong |
| author_facet | Ruipeng Chen Jiayin Liu Guangchen Zhang Xiangyu Kong |
| author_sort | Ruipeng Chen |
| collection | DOAJ |
| description | Abstract This paper is concerned with the existence of positive radial solutions of the following resonant elliptic system: { − Δ u = u v + f ( | x | , u ) , 0 < R 1 < | x | < R 2 , x ∈ R N , − Δ v = c g ( u ) − d v , 0 < R 1 < | x | < R 2 , x ∈ R N , ∂ u ∂ n = 0 = ∂ v ∂ n , | x | = R 1 , | x | = R 2 , $$ \textstyle\begin{cases} -\Delta u=uv+f( \vert x \vert ,u), & 0< R_{1}< \vert x \vert < R_{2}, x\in \mathbb{R}^{N}, \\ -\Delta v=cg(u)-dv, & 0< R_{1}< \vert x \vert < R_{2}, x\in \mathbb{R}^{N}, \\ \frac{\partial u}{\partial \textbf{n}}=0= \frac{\partial v}{\partial \textbf{n}},& \vert x \vert =R_{1}, \vert x \vert =R_{2}, \end{cases} $$ where R N $\mathbb{R}^{N}$ ( N ≥ 1 $N\geq 1$ ) is the usual Euclidean space, n indicates the outward unit normal vector, f ∈ C ( [ R 1 , R 2 ] × [ 0 , ∞ ) , R ) $f\in C([R_{1},R_{2}]\times [0,\infty ),\mathbb{R})$ , g ∈ C ( [ 0 , ∞ ) , [ 0 , ∞ ) ) $g\in C([0,\infty ),[0,\infty ))$ , and c and d are positive constants. By employing the classical fixed point theory we establish several novel existence theorems. Our main findings enrich and complement those available in the literature. |
| first_indexed | 2024-12-16T09:54:09Z |
| format | Article |
| id | doaj.art-96542ee2679945699b2e73065dc00f65 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-16T09:54:09Z |
| publishDate | 2021-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-96542ee2679945699b2e73065dc00f652022-12-21T22:35:58ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-04-012021111110.1186/s13660-021-02611-0Positive radial solutions for a noncooperative resonant nuclear reactor model with sign-changing nonlinearitiesRuipeng Chen0Jiayin Liu1Guangchen Zhang2Xiangyu Kong3Department of Mathematics, North Minzu UniversityDepartment of Mathematics, North Minzu UniversityDepartment of Mathematics, North Minzu UniversityDepartment of Mathematics, North Minzu UniversityAbstract This paper is concerned with the existence of positive radial solutions of the following resonant elliptic system: { − Δ u = u v + f ( | x | , u ) , 0 < R 1 < | x | < R 2 , x ∈ R N , − Δ v = c g ( u ) − d v , 0 < R 1 < | x | < R 2 , x ∈ R N , ∂ u ∂ n = 0 = ∂ v ∂ n , | x | = R 1 , | x | = R 2 , $$ \textstyle\begin{cases} -\Delta u=uv+f( \vert x \vert ,u), & 0< R_{1}< \vert x \vert < R_{2}, x\in \mathbb{R}^{N}, \\ -\Delta v=cg(u)-dv, & 0< R_{1}< \vert x \vert < R_{2}, x\in \mathbb{R}^{N}, \\ \frac{\partial u}{\partial \textbf{n}}=0= \frac{\partial v}{\partial \textbf{n}},& \vert x \vert =R_{1}, \vert x \vert =R_{2}, \end{cases} $$ where R N $\mathbb{R}^{N}$ ( N ≥ 1 $N\geq 1$ ) is the usual Euclidean space, n indicates the outward unit normal vector, f ∈ C ( [ R 1 , R 2 ] × [ 0 , ∞ ) , R ) $f\in C([R_{1},R_{2}]\times [0,\infty ),\mathbb{R})$ , g ∈ C ( [ 0 , ∞ ) , [ 0 , ∞ ) ) $g\in C([0,\infty ),[0,\infty ))$ , and c and d are positive constants. By employing the classical fixed point theory we establish several novel existence theorems. Our main findings enrich and complement those available in the literature.https://doi.org/10.1186/s13660-021-02611-0Noncooperative modelsRadial solutionsResonanceExistenceFixed point |
| spellingShingle | Ruipeng Chen Jiayin Liu Guangchen Zhang Xiangyu Kong Positive radial solutions for a noncooperative resonant nuclear reactor model with sign-changing nonlinearities Journal of Inequalities and Applications Noncooperative models Radial solutions Resonance Existence Fixed point |
| title | Positive radial solutions for a noncooperative resonant nuclear reactor model with sign-changing nonlinearities |
| title_full | Positive radial solutions for a noncooperative resonant nuclear reactor model with sign-changing nonlinearities |
| title_fullStr | Positive radial solutions for a noncooperative resonant nuclear reactor model with sign-changing nonlinearities |
| title_full_unstemmed | Positive radial solutions for a noncooperative resonant nuclear reactor model with sign-changing nonlinearities |
| title_short | Positive radial solutions for a noncooperative resonant nuclear reactor model with sign-changing nonlinearities |
| title_sort | positive radial solutions for a noncooperative resonant nuclear reactor model with sign changing nonlinearities |
| topic | Noncooperative models Radial solutions Resonance Existence Fixed point |
| url | https://doi.org/10.1186/s13660-021-02611-0 |
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