k-dimensional nonlocal boundary-value problems at resonance

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 $f:[0,1]\times\mathbb{R}^k\to\mathbb{R}^k$, $g:[0,1]\to\mathbb{R}^k$.

Keywords

• Nonlocal boundary value problem
• perturbation method
• boundary value problem at resonance
• Neumann BVP