Electronic Journal of Differential Equations,
Vol. 2015 (2015), No. 148, pp. 1-8.
Title: k-dimensional nonlocal boundary-value problems at resonance
Author: Katarzyna Szymanska-Debowska (Lodz Univ. of Technology, Wolczanska, Poland)
Abstract:
In this article we show the existence of at least one solution to
the system of nonlocal resonant boundary-value problem
$$
x''=f(t,x), \quad x'(0)=0, \quad x'(1)=\int_{0 }^{1}x'(s)\,dg(s),
$$
where $f:[0,1]\times\mathbb{R}^k\to\mathbb{R}^k$, $g:[0,1]\to\mathbb{R}^k$.
Submitted February 2, 2015. Published June 06, 2015.
Math Subject Classifications: 34B10, 34B15.
Key Words: Nonlocal boundary value problem; perturbation method;
boundary value problem at resonance; Neumann BVP.