| Positive and Nontrivial Solutions for the Urysohn Integral Equation |
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| 引用本文： | Daniel FRANCO Gennaro INFANTE Donal O＇REGAN. Positive and Nontrivial Solutions for the Urysohn Integral Equation[J]. 数学学报(英文版), 2006, 22(6): 1745-1750. DOI: 10.1007/s10114-005-0782-3 |
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| 作者姓名： | Daniel FRANCO Gennaro INFANTE Donal O＇REGAN |
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| 作者单位： | [1]Departamento de Matemdtica Aplicada, Universidad Nacional de EducaciSn a Distancia, Apartado de Correos 60149, Madrid, 28080, Spain [2]Dipartimento di Matematica, Universita della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy [3]Department of Mathematics, National University of Ireland, Galway, Ireland |
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| 基金项目： | The first and third authors have been supported in part by Ministerio de Ciencia y Tecnologia （Spain） MTM2004- 06652-C03-03;Acknowledgments The authors thank the anonymous referee for her/his comments which help to improve the paper. This research was partially done during a visit by Daniel Franco to the National University of Ireland at Galway and the University of Glasgow. That visit was supported by Secretarfa de Estado de Universidades e InvestigaciSn （Spain）. |
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| 摘 要： |
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| 关 键 词： | Urysohn积分方程 正解 特征向量 存在性 固定点 |
| 收稿时间： | 2004-12-14 |
| 修稿时间： | 2004-12-142005-07-18 |
Positive and Nontrivial Solutions for the Urysohn Integral Equation |
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| Daniel Franco,Gennaro Infante,Donal O’regan. Positive and Nontrivial Solutions for the Urysohn Integral Equation[J]. Acta Mathematica Sinica(English Series), 2006, 22(6): 1745-1750. DOI: 10.1007/s10114-005-0782-3 |
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| Authors: | Daniel Franco Gennaro Infante Donal O’regan |
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| Affiliation: | (1) Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Apartado de Correos 60149, Madrid, 28080, Spain;(2) Dipartimento di Matematica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy;(3) Department of Mathematics, National University of Ireland, Galway, Ireland |
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| Abstract: | We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation. |
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| Keywords: | Urysohn integral equation positive solutions eigenvalues |
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