Geodesic
Systems of Inclusions Involving Fredholm Operators and Noncompact Maps
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 119-158

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Zbl MR
We consider the existence of solutions to the system of two inclusions involving Fredholm operators of nonnegative index and the so-called fundamentally restrictible maps with not necessarily convex values. We apply the technique of a solution map and, since the assumptions admit a 'dimension defect', we use the coincidence index, i.e. the homotopy invariant based on the cohomotopy theory. Two examples of applications to boundary value problems are included. 
Gabor, Dorota. Systems of Inclusions Involving Fredholm Operators and Noncompact Maps. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 119-158. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a7/
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     author = {Gabor, Dorota},
     title = {Systems of {Inclusions} {Involving} {Fredholm} {Operators} and {Noncompact} {Maps}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {119--158},
     year = {2007},
     volume = {Ser. 8, 10B},
     number = {1},
     zbl = {1129.34006},
     mrnumber = {2310962},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a7/}
}
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