Properties of monotonic solutions to half-linear second-order delay differential equations

TEMTEK P., Turarov Y.

AIMS Mathematics, cilt.10, sa.8, ss.18983-18996, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 8
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3934/math.2025848
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.18983-18996
  • Anahtar Kelimeler: half-linear differential equations, delayed argument, monotonic properties, Kneser solutions, oscillation criteria
  • Erciyes Üniversitesi Adresli: Evet

Özet

This paper establishes new monotonic properties of nonoscillatory solutions for second-order half-linear functional differential equations with delayed argument (a(r)(u′(r))m)′ = b(r)um(φ(r)) where m ∈ (0, 1). We develop several key monotonicity results for Kneser solutions and use these properties to derive criteria for the elimination of bounded nonoscillatory solutions. Our approach extends known techniques from linear differential equations to the half-linear case, providing new insights into the qualitative behavior of solutions.