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- Title
A NONLOCAL PROBLEM AT INFINITY FOR SECOND ORDER DIFFERENTIAL EQUATIONS.
- Authors
ARIZA-RUIZ, DAVID; GONZÁLEZ, CRISTÓBAL; JIMÉNEZ-MELADO, ANTONIO
- Abstract
In this paper we propose the study of a scalar integral equation of the type y(t) = g(y) + ∫∞ι (s - t)a(s)f(y(s)) ds; t ≥ 0; 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)); y(∞) = g(y); where y(∞) = ... 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.
- Subjects
DIFFERENTIAL equations; INTEGRAL equations; EXISTENCE theorems; ASYMPTOTIC theory of algebraic ideals; LINEAR equations
- Publication
Fixed Point Theory, 2017, Vol 18, Issue 2, p433
- ISSN
1583-5022
- Publication type
Article
- DOI
10.24193/fpt-ro.2017.2.34