Multi point boundary-value problems at resonance for n-order differential equations: Positive and monotone solutions
In this article, we study a complete $n$-order differential equation subject to the $(p,n-p)$ right focal boundary conditions plus an additional nonlocal constrain. We establish sufficient conditions for the existence of a family of positive and monotone solutions at resonance. The emphasis in this...
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| Format: | Article |
| Language: | English |
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Texas State University
2004-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/25/abstr.html |
| _version_ | 1811328860022636544 |
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| author | Panos K. Palamides |
| author_facet | Panos K. Palamides |
| author_sort | Panos K. Palamides |
| collection | DOAJ |
| description | In this article, we study a complete $n$-order differential equation subject to the $(p,n-p)$ right focal boundary conditions plus an additional nonlocal constrain. We establish sufficient conditions for the existence of a family of positive and monotone solutions at resonance. The emphasis in this paper is not only that the nonlinearity depends on all higher-order derivatives but mainly that the obtaining solution satisfies the above extra condition. Our approach is based on the Sperner's Lemma, proposing in this way an alternative to the classical methodologies based on fixed point or degree theory and results the introduction of a new set of quite natural hypothesis. |
| first_indexed | 2024-04-13T15:33:36Z |
| format | Article |
| id | doaj.art-d676dbc93cfe4738ae3b2f46fc31218a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-13T15:33:36Z |
| publishDate | 2004-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-d676dbc93cfe4738ae3b2f46fc31218a2022-12-22T02:41:19ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912004-02-01200425114Multi point boundary-value problems at resonance for n-order differential equations: Positive and monotone solutionsPanos K. PalamidesIn this article, we study a complete $n$-order differential equation subject to the $(p,n-p)$ right focal boundary conditions plus an additional nonlocal constrain. We establish sufficient conditions for the existence of a family of positive and monotone solutions at resonance. The emphasis in this paper is not only that the nonlinearity depends on all higher-order derivatives but mainly that the obtaining solution satisfies the above extra condition. Our approach is based on the Sperner's Lemma, proposing in this way an alternative to the classical methodologies based on fixed point or degree theory and results the introduction of a new set of quite natural hypothesis.http://ejde.math.txstate.edu/Volumes/2004/25/abstr.htmlFocal boundary value problemmulti-pointresonancevector fieldpositive monotone solutionSperner's lemmaKnaster-Kuratowski-Mazurkiewicz's principle. |
| spellingShingle | Panos K. Palamides Multi point boundary-value problems at resonance for n-order differential equations: Positive and monotone solutions Electronic Journal of Differential Equations Focal boundary value problem multi-point resonance vector field positive monotone solution Sperner's lemma Knaster-Kuratowski-Mazurkiewicz's principle. |
| title | Multi point boundary-value problems at resonance for n-order differential equations: Positive and monotone solutions |
| title_full | Multi point boundary-value problems at resonance for n-order differential equations: Positive and monotone solutions |
| title_fullStr | Multi point boundary-value problems at resonance for n-order differential equations: Positive and monotone solutions |
| title_full_unstemmed | Multi point boundary-value problems at resonance for n-order differential equations: Positive and monotone solutions |
| title_short | Multi point boundary-value problems at resonance for n-order differential equations: Positive and monotone solutions |
| title_sort | multi point boundary value problems at resonance for n order differential equations positive and monotone solutions |
| topic | Focal boundary value problem multi-point resonance vector field positive monotone solution Sperner's lemma Knaster-Kuratowski-Mazurkiewicz's principle. |
| url | http://ejde.math.txstate.edu/Volumes/2004/25/abstr.html |
| work_keys_str_mv | AT panoskpalamides multipointboundaryvalueproblemsatresonancefornorderdifferentialequationspositiveandmonotonesolutions |