Stationary nonlinear Schrödinger equations in \(\mathbb {R}^2\) with potentials vanishing at infinity (Q509583)
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scientific article; zbMATH DE number 6686406
| Language | Label | Description | Also known as |
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| English | Stationary nonlinear Schrödinger equations in \(\mathbb {R}^2\) with potentials vanishing at infinity |
scientific article; zbMATH DE number 6686406 |
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Stationary nonlinear Schrödinger equations in \(\mathbb {R}^2\) with potentials vanishing at infinity (English)
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17 February 2017
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In this paper, the authors show the existence of the bound state solution in the classical Sobolev space \(H^1\)(\(\mathbb{R}^2\)) of the stationary nonlinear Schrödinger equation (NLS) under the conditions (V) and (Q). Their approach is based on the weighted Trudinger-Moser-type inequality (see Section 4) and the classical mountain pass theorem (see Section 5).
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nonlinear Schrödinger equation
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bound state
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vanishing potentials
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Trudinger-Moser inequality
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exponential growth
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