American Institute of Mathematical Sciences

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

Semi-positone nonlocal boundary value problems of arbitrary order

 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.
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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