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Discontinuity, Nonlinearity, and Complexity 3(4) (2014) 457--465 | DOI:10.5890/DNC.2014.12.008

Vitali Vougalter$^{1}$; Vitaly Volpert$^{2}$

$^{1}$ Department ofMathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch 7701, South Africa

$^{2}$ Institute Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, 69622, France

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Abstract

Linear second order elliptic equations containing the sum of the two Laplace operators with convection terms or a free Laplacian and a Laplacian with drift are considered in Rd. The corresponding operator L may be non Fredholm, such that solvability conditions for the equation Lu = f are unknown. We obtain solvability conditions in H2 (Rd ) for the non selfadjoint problem via relating it to a self-adjoint Schrödinger type operator, for which solvability relations are derived in our preceding work [16].

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