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Positive solutions to second-order differential equations with dependence on the first-order derivative and nonlocal boundary conditions
Abstract
In this paper, we consider the existence of positive solutions for second-order differential equations with deviating arguments and nonlocal boundary conditions. By the fixed point theorem due to Avery and Peterson, we provide sufficient conditions under which such boundary value problems have at least three positive solutions. We discuss our problem both for delayed and advanced arguments α and also in the case when α(t)=t, t∈[0,1]. In all cases, the argument β can change the character on [0,1], see problem (1). It means that β can be delayed in some set J¯⊂[0,1] and advanced in [0,1]∖J¯. An example is added to illustrate the results.
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1186/1687-2770-2013-8
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
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Boundary Value Problems
pages 1 - 21,
ISSN: 1687-2770 - Language:
- English
- Publication year:
- 2013
- Bibliographic description:
- Jankowski T.: Positive solutions to second-order differential equations with dependence on the first-order derivative and nonlocal boundary conditions// Boundary Value Problems. -, iss. 1 (2013), s.1-21
- DOI:
- Digital Object Identifier (open in new tab) 10.1186/1687-2770-2013-8
- Verified by:
- Gdańsk University of Technology
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