American Institute of Mathematical Sciences

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March  2010, 9(2): 563-581. doi: 10.3934/cpaa.2010.9.563

Semi-positone nonlocal boundary value problems of arbitrary order

J. R. L. Webb 1, and  Gennaro Infante 2,

1. 

Department of Mathematics, University of Glasgow, Glasgow G12 8QW
2. 

Dipartimento di Matematica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza

Received  December 2008 Revised  August 2009 Published  December 2009

We give a unified approach to the study of existence of multiple positive solutions for semi-positone boundary value problems of arbitrary order. We cover local and nonlocal boundary conditions. Our nonlocal boundary conditions are quite general, they involve positive linear functionals on the space $C[0,1]$, given by Stieltjes integrals. With our general theory, we can, for the first time in semi-positone problems, allow any number of the boundary conditions to be nonlocal.
Keywords: positive solution., Nonlocal boundary conditions, semi-positone.
Mathematics Subject Classification: Primary: 34B18; Secondary: 34B10, 47H11, 47H3.
Citation: J. R. L. Webb, Gennaro Infante. Semi-positone nonlocal boundary value problems of arbitrary order. Communications on Pure & Applied Analysis, 2010, 9 (2) : 563-581. doi: 10.3934/cpaa.2010.9.563
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