Nonlinear alternatives of hybrid type for nonself vector-valued maps and application



	Nonlinear alternatives of hybrid type for nonself vector-valued maps and application


	Fixed Point Theory, Volume 24, No. 1, 2023, 221-232, February 1st, 2023 DOI: 10.24193/fpt-ro.2023.1.11 Authors: Veronica Ilea, Adela Novac, Diana Otrocol and Radu Precup Abstract: In this paper we obtain nonlinear alternatives of Leray-Schauder and Mönch type for nonself vector-valued operators, under hybrid conditions of Perov contraction and compactness. Thus, we give vector versions of the theorems of Krasnosel'skii, Avramescu, Burton-Kirk and Gao-Li-Zhang. An application is given to a boundary value problem for a system of second order differential equations in which some of the equations are implicit. Key Words and Phrases: Nonlinear operator, nonself map, fixed point, Perov contraction, nonlinear boundary value problem. 2010 Mathematics Subject Classification: 47H10, 34B15. Published on-line: February 1st, 2023. Fulltext pdf Back to volume's table of contents