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2018•Differential Equations & ApplicationsOpen access

Existence and uniqueness of solutions of Schrödinger type stationary equations with very singular potentials without prescribing boundary conditions and some applications

Jesús Ildefonso Díaz Díaz, David Gómez‐Castro, Jean‐Michel Rakotoson

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Abstract

Motivated mainly by the localization over an open bounded set of R n of solutions of the Schrdinger equations, we consider the Schrdinger equation over with a very singular potential V (x) Cd(x, ) -r with r 2 and a convective flow U . We prove the existence and uniqueness of a very weak solution of the equation, when the right hand side datum

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Motivated mainly by the localization over an open bounded set of R n of solutions of the Schrdinger equations, we consider the Schrdinger equation over with a very singular potential V (x) Cd(x, ) -r with r 2 and a convective flow U . We prove the existence and uniqueness of a very weak solution of the equation, when the right hand side datum

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Available abstract

Motivated mainly by the localization over an open bounded set of R n of solutions of the Schrdinger equations, we consider the Schrdinger equation over with a very singular potential V (x) Cd(x, ) -r with r 2 and a convective flow U . We prove the existence and uniqueness of a very weak solution of the equation, when the right hand side datum

Key concepts: Uniqueness, Omega, Mathematics, Dirichlet boundary condition, Boundary (topology), Dirichlet problem, Bounded function, Type (biology)

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