Existence of a positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in \({\mathbb{R}^{2}}\) (Q302412)
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scientific article; zbMATH DE number 6600835
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of a positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in \({\mathbb{R}^{2}}\) |
scientific article; zbMATH DE number 6600835 |
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Existence of a positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in \({\mathbb{R}^{2}}\) (English)
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5 July 2016
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The author is concerned with the study of \(-\varepsilon^2 \Delta u+V(x) u=f(u)\) in \({\mathbb R}^2\), where \(f\) has an exponential growth, \(V\) is a saddle-like potential and \(\varepsilon>0\). By using variational methods the author establishes the existence of a positive solution.
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variational methods
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positive solutions
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elliptic equation
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