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# Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 4

# System of nonlocal resonant boundary value problems involving p-Laplacian

Katarzyna Szymańska-Dębowska
Published Online: 2018-08-06 | DOI: https://doi.org/10.1515/ms-2017-0149

## Abstract

Our aim is to study the existence of solutions for the following system of nonlocal resonant boundary value problem

$(φ(x′))′=f(t,x,x′),x′(0)=0,x(1)=∫01x(s)dg(s),$

where the function ϕ : ℝn → ℝn is given by ϕ (s) = (φp1(s1), …, φpn(sn)), s ∈ ℝn, pi > 1 and φpi : ℝ → ℝ is the one dimensional pi -Laplacian, i = 1,…,n, f : [0,1] × ℝn × ℝn → ℝn is continuous and g : [0,1] → ℝn is a function of bounded variation. The proof of the main result is depend upon the coincidence degree theory.

MSC 2010: Primary 34B10; 34B15; 34K10; 54H25

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Accepted: 2017-04-18

Published Online: 2018-08-06

Published in Print: 2018-08-28

Communicated by Michal Fečkan

Citation Information: Mathematica Slovaca, Volume 68, Issue 4, Pages 837–844, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918,

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