Existence of ground states for nonlinear, pseudo-relativistic Schrödinger equations (Q545895)
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scientific article; zbMATH DE number 5912110
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of ground states for nonlinear, pseudo-relativistic Schrödinger equations |
scientific article; zbMATH DE number 5912110 |
Statements
Existence of ground states for nonlinear, pseudo-relativistic Schrödinger equations (English)
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23 June 2011
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Summary: We study existence and regularity of positive stationary solutions for a class of nonlinear pseudo-relativistic Schrödinger equations. Such equations are characterized by a nonlocal pseudo-differential operator closely related to the square-root of the Laplacian. We investigate such problems using critical point theory after transforming them to elliptic equations with nonlinear Neumann boundary conditions.
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nonlinear Schrödinger equation
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solitary waves
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pseudo-relativistic Hartree approximation
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