Abstract
We study solvability of certain linear nonhomogeneous elliptic problems and establish that under reasonable technical assumptions the convergence in \(L^{2}({\mathbb R}^{d})\) of their right sides implies the existence and the convergence in \(H^{1}({\mathbb R}^{d})\) of the solutions. The equations involve the square roots of the sums of second order non-Fredholm differential operators and we rely on the methods of the spectral and scattering theory for Schrödinger type operators similarly to our earlier work [26].
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Vougalter, V., Volpert, V. (2021). Solvability in the Sense of Sequences for Some Non-Fredholm Operators in Higher Dimensions. In: Volchenkov, D. (eds) Nonlinear Dynamics, Chaos, and Complexity. Nonlinear Physical Science. Springer, Singapore. https://doi.org/10.1007/978-981-15-9034-4_11
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DOI: https://doi.org/10.1007/978-981-15-9034-4_11
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