On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals

• Autorzy: Aneta Sikorska-Nowak
• Języki publikacji: EN

Abstrakty

EN

We prove some existence theorems for nonlinear integral equations of the Urysohn type $x(t) = φ(t) + λ∫_0^a f(t,s,x(s))ds$ and Volterra type $x(t) = φ(t) + ∫_0^tf(t,s,x(s))ds$, $t ∈ I_a = [0,a]$, where f and φ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.

Kategorie tematyczne

• 28B05: Vector-valued set functions, measures and integrals
• 34G20: Nonlinear equations
• 45D05: Volterra integral equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2004
• Tom: 83
• Numer: 3
• Strony: 257-267

Daty

wydano

2004

Twórcy

autor

Aneta Sikorska-Nowak

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

Identyfikatory

DOI

10.4064/ap83-3-7