A nonlocal problem at infinity for second order differential equations


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	A nonlocal problem at infinity for second order differential equations


	Fixed Point Theory, Volume 18, No. 2, 2017, 433-444, June 1st, 2017 DOI: 10.24193/fpt-ro.2017.2.34 Authors: D. Ariza-Ruiz, C. González and A. Jiménez-Melado Abstract: In this paper we propose the study of a scalar integral equation of the type $y(t) =g(y)+\int_t^\infty (s-t)a(s)f(y(s))\,ds, t\geq0,$ and give conditions on g, a and f that ensure the existence of solutions on [0,∞) which are asymptotically equal to g(y) at ∞. As a consequence, we obtain results on the existence of solutions for a problem of the type $y''(t)=a(t)f(y(t)) , \quad y(\infty )=g(y),$ where $y(\infty)=\lim\limits_{t\to\infty}y(t)$ . This problem could be thought as a sort of nonlocal problem at ∞, and our conditions on f include the case of a linear equation. Key Words and Phrases: Nonlocal problem, asymptotic behavior, integral equation, second order differential equation, Leray-Schauder type fixed point theorem. 2010 Mathematics Subject Classification: 34A34, 45M05, 47H10, 47N20. Published on-line: June 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents