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On the Oscillation of Even-Order Half-Linear Functional Difference Equations with Damping Term

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dc.contributor.authorBolat, Yaşar
dc.contributor.authorAlzabut, Jehad
dc.date.accessioned2026-01-05T23:19:34Z
dc.date.issued2014-01-01
dc.description.abstractWe investigate the oscillatory behavior of solutions of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>th order half-linear functional difference equations with damping term of the form<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>[p</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>Q</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">]</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>Q</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>Q</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>τ</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>, where<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>is even and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mi>Q</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mfenced open="|" close="|" separators="|"><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>α</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>s</mml:mi></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mi>α</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn></mml:math>is a fixed real number. Our main results are obtained via employing the generalized Riccati transformation. We provide two examples to illustrate the effectiveness of the proposed results.
dc.description.urihttps://doi.org/10.1155/2014/791631
dc.description.urihttps://downloads.hindawi.com/journals/ijde/2014/791631.pdf
dc.description.urihttps://zbmath.org/6309766
dc.description.urihttps://doaj.org/article/5f794e46df1842389318e725d8ef63d1
dc.description.urihttps://dx.doi.org/10.1155/2014/791631
dc.description.urihttp://projecteuclid.org/euclid.ijde/1484881401
dc.identifier.doi10.1155/2014/791631
dc.identifier.eissn1687-9651
dc.identifier.endpage6
dc.identifier.issn1687-9643
dc.identifier.openairedoi_dedup___::ab14bf089cbc71c1368d7e4ea67c238e
dc.identifier.orcid0000-0002-5262-1138
dc.identifier.scopus2-s2.0-85057052600
dc.identifier.startpage1
dc.identifier.urihttps://hdl.handle.net/20.500.12597/43719
dc.identifier.volume2014
dc.identifier.wos000214965300029
dc.language.isoeng
dc.publisherWiley
dc.relation.ispartofInternational Journal of Differential Equations
dc.rightsOPEN
dc.subjectOscillation theory for difference equations
dc.subjectQA1-939
dc.subjectDiscrete version of topics in analysis
dc.subjectMathematics
dc.subjectAdditive difference equations
dc.subject.sdg16. Peace & justice
dc.titleOn the Oscillation of Even-Order Half-Linear Functional Difference Equations with Damping Term
dc.typeArticle
dspace.entity.typePublication
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