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Mathematica Slovaca

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Volume 68, Issue 4

Issues

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

Keywords: nonlocal boundary conditions; resonant problem; nonlinear problem; p-Laplacian; coincidence theory

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About the article

Received: 2016-12-19

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, DOI: https://doi.org/10.1515/ms-2017-0149.

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