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Existence of solutions for a perturbed problem with logarithmic potential in $\mathbb{R}^2$

Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, via Roberto Cozzi 55, I-20125, Milano, Italy

This contribution is part of the Special Issue: Qualitative Analysis and Spectral Theory for Partial Differential Equations
Guest Editor: Veronica Felli
Link: http://www.aimspress.com/newsinfo/1371.html

Special Issues: Qualitative Analysis and Spectral Theory for Partial Differential

We study a perturbed Schrödinger equation in the plane arising from the coupling of quantum physics with Newtonian gravitation. We obtain some existence results by means of a perturbation technique in Critical Point Theory.
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Keywords variational methods; perturbation methods; finite-dimensional reduction

Citation: Federico Bernini, Simone Secchi. Existence of solutions for a perturbed problem with logarithmic potential in $\mathbb{R}^2$. Mathematics in Engineering, 2020, 2(3): 438-458. doi: 10.3934/mine.2020020


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