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Solvability conditions for some systems with non Fredholm operators. (English) Zbl 1399.35152

Summary: We derive solvability conditions in \(H^2\) (\(\mathbb R^3; \mathbb R^2\)) for certain systems of nonhomogeneous elliptic partial differential equations involving Schrödinger type operators without Fredholm property using the technique developed in preceding works [V. Vougalter and V. Volpert, Proc. Edinb. Math. Soc., II. Ser. 54, No. 1, 249–271 (2011; Zbl 1217.35203); Int. J. Pure Appl. Math. 60, No. 2, 169–191 (2010; Zbl 1196.35075);“Solvability relations for some non Fredholm operators”, Int. Electron. J. Pure Appl. Math. 2, No. 1, 75–83 (2010); Commun. Pure Appl. Anal. 11, No. 1, 365–373 (2012; Zbl 1264.35103); Rend. Ist. Mat. Univ. Trieste 43, 1–9 (2011; Zbl 1254.35234)].

MSC:

35J10 Schrödinger operator, Schrödinger equation
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35P25 Scattering theory for PDEs
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