Geodesic
On Nonlinear Systems of BVPs with Positive Green's Functions
Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 607-642

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This paper provides some existence and uniqueness theorems for nonlinear systems of BVPs where the Green's functions for the linearization have constant sign (hence these results apply, e.g., to Dirichlet problems for elliptic PDEs as well as to various multipoint BVPs for higher order ODEs). Proofs are based on an original way of using the Linear Functional Analysis of ordered Banach spaces in connection with the traditional topological methods of Nonlinear Functional Analysis. 
Vidossich, Giovanni. On Nonlinear Systems of BVPs with Positive Green's Functions. Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 607-642. http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a7/
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     author = {Vidossich, Giovanni},
     title = {On {Nonlinear} {Systems} of {BVPs} with {Positive} {Green's} {Functions}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {607--642},
     year = {2013},
     volume = {Ser. 9, 6},
     number = {3},
     mrnumber = {3202843},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a7/}
}
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