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AIMS Mathematics

2025, Volume 10, Issue 11: 27044-27057. doi: 10.3934/math.20251188
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Existence and nonexistence outcomes for a third-order $ q $-difference equation

  • 1.
    Department of Mathematics, Istanbul Beykent University, İstanbul 34500, Türkiye; Email: nihanturan@beykent.edu.tr
  • 2.
    Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Türkiye
  • Published: 21 November 2025

  • MSC : 39A13, 47H10

  • In this paper, using the Schauder and the Banach fixed point (FP) theorems, we examine the existence and uniqueness of solutions in the Banach space $ C([0, 1]) $ for a boundary value problem (BVP) of non-linear third-order $ q $-difference equations with the $ q $-integral boundary condition. Then, we impose the sufficient condition that allows us to deduce a nonexistence result. Furthermore, we offer some examples to support our main outcomes.

    Citation: Nihan Turan, Aynur Şahin. Existence and nonexistence outcomes for a third-order $ q $-difference equation[J]. AIMS Mathematics, 2025, 10(11): 27044-27057. doi: 10.3934/math.20251188

    Related Papers:

  • In this paper, using the Schauder and the Banach fixed point (FP) theorems, we examine the existence and uniqueness of solutions in the Banach space $ C([0, 1]) $ for a boundary value problem (BVP) of non-linear third-order $ q $-difference equations with the $ q $-integral boundary condition. Then, we impose the sufficient condition that allows us to deduce a nonexistence result. Furthermore, we offer some examples to support our main outcomes.



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