Monotone positive solutions of impulsive differential equations asymptotic to nonprincipal solutions

DOĞRU AKGÖL S., Zafer A.

Turkish Journal of Mathematics, cilt.49, sa.6, ss.838-849, 2025 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.55730/1300-0098.3628
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.838-849
  • Anahtar Kelimeler: asymptotic integration, impulse, monotone, positive, principal and nonprincipal solution, Second order
  • Çukurova Üniversitesi Adresli: Evet

Özet

This study investigates the asymptotic behavior of monotone positive solutions for a general class of nonlinear second-order impulsive differential equations. By employing the principal and nonprincipal solutions of the associated homogeneous equation, we establish the existence of a monotone positive solution asymptotic to a nonprincipal solution at infinity. To achieve this, we also prove a compactness criterion for an effective use of Schauder’s fixed-point theorem. Under suitable conditions, similarly to the classical case, it is demonstrated that a monotone positive solution asymptotic to a nonprincipal solution exists. A concrete example is given to illustrate the results.