Electron. J. Diff. Equ., Vol. 2015 (2015), No. 148, pp. 1-8.

k-dimensional nonlocal boundary-value problems at resonance

Katarzyna Szymanska-Debowska

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 6, 2015.
Math Subject Classifications: 34B10, 34B15.
Key Words: Nonlocal boundary value problem; perturbation method; boundary value problem at resonance; Neumann BVP.

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Katarzyna Szymanska-Debowska
Institute of Mathematics
Lodz University of Technology
90-924 Lodz, ul. Wolczanska 215, Poland
email: katarzyna.szymanska-debowska@p.lodz.pl

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