Geodesic
Boundary-value problems for the inhomogeneous Schr\"odinger equation with variations of its potential on non-compact Riemannian manifolds
Problemy analiza, Tome 10 (2021) no. 3, pp. 113-128

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We study solutions of the inhomogeneous Schrödinger equation $\Delta u-c(x)u=g(x)$, where $c(x)$, $g(x)$ are Hölder functions, with variations of its potential $ c(x)\geq 0 $ on a noncompact Riemannian manifold $M$. Our technique essentially relies on an approach from the papers by E. A. Mazepa and S. A. Korol’kov connected with introduction of equivalency classes of functions. It made it possible to formulate boundary-value problems on $M$ independently from a natural geometric compactification. In the present work, we obtain conditions under which the solvability of boundary-value problems of the inhomogeneous Schrödinger equation is preserved for some variations of the coefficient $c(x) \geq 0$ on $M$.
Keywords: inhomogeneous Schrödinger equation, boundary-value problems, Riemannian manifold.
Mots-clés : variations of coefficients 
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     author = {E. A. Mazepa and D. K. Ryaboshlykova},
     title = {Boundary-value problems for the inhomogeneous {Schr\"odinger} equation with variations of its potential on non-compact {Riemannian} manifolds},
     journal = {Problemy analiza},
     pages = {113--128},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2021_10_3_a8/}
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E. A. Mazepa; D. K. Ryaboshlykova. Boundary-value problems for the inhomogeneous Schr\"odinger equation with variations of its potential on non-compact Riemannian manifolds. Problemy analiza, Tome 10 (2021) no. 3, pp. 113-128. http://geodesic.mathdoc.fr/item/PA_2021_10_3_a8/