Existence of positive solutions of some integral equations

Jan Ligęza

Published: 2004-09-30

Vol. 18 (2004)

Existence of positive solutions of some integral equations

Jan Ligęza

Abstract

We study the existence of positive solutions of the integral equation
x(t) = ∫₀¹k(t,s)f(s,x(s),x'{s),...,x^(n-1)(s))ds, n≥2
in both Cⁿ^-1[0,1] and Wⁿ^-1,p[0,1] spaces, where p≥1. The Krasnosielskii fixed point theorem on cone is used.

Keywords:

boundary value problems , positive solutions , Fredholm integral equations , cone , fixed point theorem

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Ligęza, J. (2004). Existence of positive solutions of some integral equations. Annales Mathematicae Silesianae, 18, 21–38. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14089

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Vol. 18 (2004)
Published: 2004-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

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