Existence of solutions for some nonautonomous partial functional differential equations with state-dependent delay

• Moussa El-Khalil Kpoumiè ^[1] ; Abdel Hamid Gamal Nsangou ^[2] ; Salifou Mboutngam ^[2] ; Patrice Ndambomve ^[3] ; Issa Zabsonre ^[4]
  1. [1] Universidad de Ngaoundéré
  2. [2] Universidad de Maroua
  3. [3] Universidad de Buea
  4. [4] Universidad de Uagadugú

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• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 77, Nº. 2, 2020, págs. 107-118
• Idioma: inglés
• DOI: 10.1007/s40324-019-00206-w
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• Resumen

  • The aim of this work is to prove the existence of mild solutions for some nondensely nonautonomous partial functional differential equations with state-dependent delay in Banach spaces. We assume that the linear part is not necessarily densely defined and generates an evolution family. Our approach is based on a nonlinear alternative of Leray–Schauder type and nonautonomous evolution family with nondensely domain. We propose a reaction diffusion equation with state-dependent delay to illustrate the obtained result.