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On the solvability in the sense of sequences for some non-Fredholm operators

Vitali Vougalter 1 Vitaly Volpert 2, 3 
2 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
3 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We investigate solvability of certain linear nonhomogeneous elliptic equations and establish that under reasonable technical conditions the convergence in L-2(R-d) of their right sides yields the existence and the convergence in H-2(R-d) of the solutions. The problems involve the sums of second order differential operators without Fredholm property and we apply the methods of spectral and scattering theory for Schrodinger type operators analogously to our previous work [18].
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https://hal.inria.fr/hal-01096776
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Submitted on : Thursday, December 18, 2014 - 11:24:26 AM
Last modification on : Monday, May 16, 2022 - 3:12:02 PM

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Vitali Vougalter, Vitaly Volpert. On the solvability in the sense of sequences for some non-Fredholm operators. Dynamics of Partial Differential Equations, International Press, 2014, 11 (2), pp.109-124. ⟨10.4310/DPDE.2014.v11.n2.a1⟩. ⟨hal-01096776⟩

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