Accessible Unlicensed Requires Authentication Published by De Gruyter March 25, 2015

On the existence of solutions for nonlocal boundary value problems

Katarzyna Szymańska-Dębowska


This paper deals with the existence of solutions for a system of k equations x''=f(t,x,x'), where f:[0,1]×k×kk is a vector function, subject to various nonlocal boundary conditions. The method is to impose an a priori bound condition on f and apply the Leray–Schauder fixed point theorem. Our results extend some results in the references and also provide the information on the existence of stationary solutions for the heat equation with nonlinear gradient source terms.

Received: 2013-8-30
Revised: 2014-3-6
Accepted: 2014-3-7
Published Online: 2015-3-25
Published in Print: 2015-6-1

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