Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales

Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales

A four-functional fixed point theorem and a generalization of Leggett-Williams fixed point theorem are used, respectively, to investigate the existence of at least one positive solution and at least three positive solutions for third-order -point boundary value problem on time scales with an increas...

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Main Authors: Fatma Tokmak, Ilkay Yaslan Karaca
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/506716
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spelling doaj-0c6da8661d644b728b336ab841d4cc0e2020-11-25T01:10:31ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/506716506716Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time ScalesFatma Tokmak0Ilkay Yaslan Karaca1Department of Mathematics, Ege University, Izmir, 35100 Bornova, TurkeyDepartment of Mathematics, Ege University, Izmir, 35100 Bornova, TurkeyA four-functional fixed point theorem and a generalization of Leggett-Williams fixed point theorem are used, respectively, to investigate the existence of at least one positive solution and at least three positive solutions for third-order -point boundary value problem on time scales with an increasing homeomorphism and homomorphism, which generalizes the usual -Laplacian operator. In particular, the nonlinear term is allowed to change sign. As an application, we also give some examples to demonstrate our results.http://dx.doi.org/10.1155/2012/506716
collection DOAJ
language English
format Article
sources DOAJ
author Fatma Tokmak
Ilkay Yaslan Karaca
spellingShingle Fatma Tokmak
Ilkay Yaslan Karaca
Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales
Abstract and Applied Analysis
author_facet Fatma Tokmak
Ilkay Yaslan Karaca
author_sort Fatma Tokmak
title Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales
title_short Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales
title_full Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales
title_fullStr Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales
title_full_unstemmed Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales
title_sort existence of positive solutions for third-order -point boundary value problems with sign-changing nonlinearity on time scales
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description A four-functional fixed point theorem and a generalization of Leggett-Williams fixed point theorem are used, respectively, to investigate the existence of at least one positive solution and at least three positive solutions for third-order -point boundary value problem on time scales with an increasing homeomorphism and homomorphism, which generalizes the usual -Laplacian operator. In particular, the nonlinear term is allowed to change sign. As an application, we also give some examples to demonstrate our results.
url http://dx.doi.org/10.1155/2012/506716
work_keys_str_mv AT fatmatokmak existenceofpositivesolutionsforthirdorderpointboundaryvalueproblemswithsignchangingnonlinearityontimescales
AT ilkayyaslankaraca existenceofpositivesolutionsforthirdorderpointboundaryvalueproblemswithsignchangingnonlinearityontimescales
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