| Existence of Positive Solutions to Semipositone Singular Dirichlet Boundary Value Problems |
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| 引用本文： | Svatoslav STANEK. Existence of Positive Solutions to Semipositone Singular Dirichlet Boundary Value Problems[J]. 数学学报(英文版), 2006, 22(6): 1891-1914. DOI: 10.1007/s10114-005-0843-7 |
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| 作者姓名： | Svatoslav STANEK |
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| 作者单位： | Department of Mathematical Analysis, Faculty of Science, Palacky University, Tomkova 40, 77900 Olomouc, Czech Republic |
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| 基金项目： | This work is supported by Grant No. 201/04/1077 of the, Grant Agency of Czech Republic and by the Uouncn of Czech Government MSM 6198959214 |
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| 摘 要： | The paper presents the conditions which guarantee that for some positive value of μ there are positive solutions of the differential equation （Ф（x＇））＇＋μQ（t, x, x＇） = 0 satisfying the Dirichlet boundary conditions x（0） = x（T） = 0. Here Q is a continuous function on the set [0, T] × （0, ∞） ~ （R ／ {0}） of the semipositone type and Q is singular at the value zero of its phase variables.
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| 关 键 词： | 存在性 正解 单一问题 Dirichlet边界情况 Ф-拉普拉斯算子 |
| 收稿时间： | 2005-07-27 |
| 修稿时间： | 2005-07-272006-03-14 |
Existence of Positive Solutions to Semipositone SingularDirichlet Boundary Value Problems |
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| Svatoslav Staněk. Existence of Positive Solutions to Semipositone SingularDirichlet Boundary Value Problems[J]. Acta Mathematica Sinica(English Series), 2006, 22(6): 1891-1914. DOI: 10.1007/s10114-005-0843-7 |
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| Authors: | Svatoslav Staněk |
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| Affiliation: | (1) Department of Mathematical Analysis, Faculty of Science, Palacky University, Tomkova 40, 77900 Olomouc, Czech Republic |
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| Abstract: | The paper presents the conditions which guarantee that for some positive value of ì there are positive solutions of the di.erential equation (φ(x'))'+μQ(t, x, x') = 0 satisfying the Dirichlet boundary conditions x(0) = x(T) = 0. Here Q is a continuous function on the set [0, T] × (0,∞) × (ℝ {0}) of the semipositone type and Q is singular at the value zero of its phase variables. This work is supported by Grant No. 201/04/1077 of the Grant Agency of Czech Republic and by the Council of Czech Government MSM 6198959214 |
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| Keywords: | existence positive solution semipositone singular problem Dirichlet boundary conditions φ -Laplacian |
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