In this paper, a careful analysis on the existence of a priori bounded solutions for difference equations is provided. In particular, we study a second order nonlinear difference boundary value problem and its relationship with the continuous one and we obtain a version of these existence results with a priori bounds of the solution u and its derivative u ', u '' and we give an analytic expression of the solution u as the limit of a suitable sequence of functions.
Amoroso E., Candito P., Mawhin J. (2023). Existence of a priori bounded solutions for discrete two-point boundary value problems. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 519(2) [10.1016/j.jmaa.2022.126807].
Existence of a priori bounded solutions for discrete two-point boundary value problems
Amoroso E.
;Candito P.;
2023-03-15
Abstract
In this paper, a careful analysis on the existence of a priori bounded solutions for difference equations is provided. In particular, we study a second order nonlinear difference boundary value problem and its relationship with the continuous one and we obtain a version of these existence results with a priori bounds of the solution u and its derivative u ', u '' and we give an analytic expression of the solution u as the limit of a suitable sequence of functions.
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