| 著作名稱： | Complete classification of bifurcation curves for a multiparameter diffusive logistic problem with generalized Holling type-IV functional response |
| 年度： | 2021 |
| 類別： |
期刊論文
Electronic Journal of Differential Equations
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| 摘要： | We study exact multiplicity and bifurcation curves of positive solutions for the diffusive logistic problem with generalized Holling type-IV functional response. We give a complete classi fication of two qualitatively different bifurcation curves: a C-shaped curve and a monotone increasing curve. Hence we are able to determine the exact multiplicity of positive solutions for the diffusive logistic problem. |
| 關鍵字： | Bifurcation curve; exact multiplicity; diffusive logistic problem; Holling type-IV functional response; time map. |
| 著作名稱： | S-shaped and broken S-shaped bifurcation curves for a multiparameter diffusive logistic problem with Holling type-III functional response |
| 年度： | 2017 |
| 類別： |
期刊論文
Communications on Pure and Applied Analysis
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| 摘要： | We study exact multiplicity and bifurcation curves of positive solutions for a multiparameter diffusive logistic problem with Holling type-III functional response. We give a classification of four qualitatively different bifurcation curves: an S-shaped curve, a broken S-shaped curve, a ⊂-shaped curve and a monotone increasing curve. |
| 關鍵字： | S-shaped bifurcation curve, broken S-shaped bifurcation curve, Holling type-III functional response, diffusive logistic problem, time map |
| 著作名稱： | Bifurcation curves of positive steady-state solutions for a reaction-diffusion problem of lake eutrophication |
| 年度： | 2017 |
| 類別： |
期刊論文
Journal of Mathematical Analysis and Applications
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| 摘要： | |
| 關鍵字： | |
| 著作名稱： | Classification of bifurcation curves of positive solutions for a nonpositone problem with a quartic polynomial |
| 年度： | 2016 |
| 類別： |
期刊論文
Communications on Pure and Applied Analysis
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| 摘要： | We study exact multiplicity and bifurcation curves of positive solutions for a nonpositone problem with a quartic polynomial, we give a classification of four qualitatively different bifurcation curves: an S-shaped curve, a broken S-shaped curve, a ⊂-shaped curve and a monotone increasing curve. |
| 關鍵字： | S-shaped bifurcation curve, broken S-shaped bifurcation curve, exact multiplicity, nonpositone problem, quartic polynomial, time map |
| 著作名稱： | Classification of bifurcation diagrams for a multiparameter diffusive logistic problem with Holling type-IV functional response |
| 年度： | 2014 |
| 類別： |
期刊論文
Journal of Mathematical Analysis and Applications
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| 摘要： | We study exact multiplicity and bifurcation diagrams of positive solutions for a multiparameter diffusive logistic problem with Holling type-IV functional response. Under some assumptions, we give a classification of four qualitatively different bifurcation diagrams: an S-shaped curve, a broken S-shaped curve, a ㄈ-shaped curve and a monotone increasing curve. |
| 關鍵字： | S-shaped bifurcation diagram; Broken S-shaped bifurcation diagram; Exact multiplicity; Diffusive logistic problem; Holling type-IV functional response; Time map |
| 著作名稱： | Classification of bifurcation diagrams of a p-Laplacian nonpositone problem |
| 年度： | 2013 |
| 類別： |
期刊論文
Communications on Pure and Applied Analysis
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| 摘要： | We study the bifurcation diagrams of positive solutions of a p-Laplacian Dirichlet problem. Under certain hypotheses, we give a complete classification of bifurcation diagrams. We prove that, each bifurcation diagram consists of exactly one curve which has exactly one turning point where the curve turns to the right. In addition, we show the evolution phenomena of bifurcation diagrams of polynomial nonlinearities with positive coefficients. |
| 關鍵字： | Bifurcation diagram, positive solution, p-Laplacian, nonpositone problem, exact multiplicity |
| 著作名稱： | S-shaped and broken S-shaped bifurcation diagrams with hysteresis for a multiparameter spruce budworm population problem in one space dimension |
| 年度： | 2013 |
| 類別： |
期刊論文
Journal of Differential Equations
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| 摘要： | We study exact multiplicity and bifurcation diagrams of positive solutions for a multiparameter spruce budworm population steady-state problem in one space dimension.
We give a classification of three qualitatively different bifurcation diagrams: an S-shaped curve, a broken S-shaped curve, and a monotone increasing curve. Our results settle rigorously a long-standing open problem in Ludwig, Aronson and Weinberger (J. Math. Biol., 8 (1979), pp. 217258). |
| 關鍵字： | S-shaped bifurcation diagram; Broken S-shaped bifurcation diagram; Weak hysteresis; Strong hysteresis; Spruce budworm problem; Time map |
| 著作名稱： | Classification of bifurcation diagrams of a p-Laplacian Dirichlet problem with examples |
| 年度： | 2010 |
| 類別： |
期刊論文
Journal of Mathematical Analysis and Applications
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| 摘要： | |
| 關鍵字： | |
| 著作名稱： | A theorem on reversed S-shaped bifurcation curves for a class of boundary value problems and its application |
| 年度： | 2009 |
| 類別： |
期刊論文
Nonlinear Analysis: Theory Methods & Applications
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| 摘要： | |
| 關鍵字： | |
| 著作名稱： | Exact multiplicity of solutions and S-shaped bifurcation curves for the p-Laplacian perturbed Gelfand problem in one space variable |
| 年度： | 2008 |
| 類別： |
期刊論文
Journal of Mathematical Analysis and Applications
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| 摘要： | |
| 關鍵字： | |
| 著作名稱： | Exact structure of positive solutions for a p-Laplacian problem involving singular and superlinear nonlinearities |
| 年度： | 2007 |
| 類別： |
期刊論文
Rocky Mountain Journal of Mathematics
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| 摘要： | |
| 關鍵字： | |
| 著作名稱： | The structure of the solution set of a generalized Ambrosetti-Brezis-Cerami problem in one space variable |
| 年度： | 2006 |
| 類別： |
期刊論文
Journal of Mathematical Analysis and Applications
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| 摘要： | |
| 關鍵字： | |
| 著作名稱： | A complete classification of bifurcation diagrams of a p-Laplacian Dirichlet problem |
| 年度： | 2006 |
| 類別： |
期刊論文
Nonlinear Analysis: Theory Methods & Applications
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| 摘要： | |
| 關鍵字： | |
| 著作名稱： | On the exact structure of positive solutions of an Ambrosetti-Brezis-Cerami problem and its generalization in one space variable |
| 年度： | 2004 |
| 類別： |
期刊論文
Differential and Integral Equations
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| 摘要： | |
| 關鍵字： | |
| 著作名稱： | A complete classification of bifurcation diagrams of a Dirichlet problem with concave-convex nonlinearities |
| 年度： | 2004 |
| 類別： |
期刊論文
Journal of Mathematical Analysis and Applications
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| 摘要： | |
| 關鍵字： | |
| 著作名稱： | Exact multiplicity and ordering properties of positive solutions of a p-Laplacian Dirichlet problem and their applications |
| 年度： | 2003 |
| 類別： |
期刊論文
Journal of Mathematical Analysis and Applications
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| 摘要： | |
| 關鍵字： | |