On the Behaviors of Solutions of Linear Nonhomogeneous Mixed Type Differential Equations

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Yeniçerioğlu A. F.

Turkish Journal of Mathematics and Computer Science, vol.2026, pp.1-13, 2026 (Scopus, TRDizin)

• Publication Type: Article / Article
• Volume: 2026
• Publication Date: 2026
• Journal Name: Turkish Journal of Mathematics and Computer Science
• Journal Indexes: Scopus, TR DİZİN (ULAKBİM)
• Page Numbers: pp.1-13
• Kocaeli University Affiliated: Yes

Abstract

This paper deals with the behaviors of solutions for nonhomogeneous linear mixed-type (delay and

advance) differential equations. In this study, an asymptotic result and a useful exponential estimate for the solutions

are established. Additionally, stability criteria for the homogeneous equation are also obtained. We obtained these

results using a real root (with a suitable property) of the characteristic equation. We present three examples to

illustrate the hypotheses of these results. We also obtain useful lemmas that give sufficient conditions for the

existence of the roots of the characteristic equation.