In this paper we study the equation (Formula presented.) where 8/3<4. By means of variational arguments, we find infinitely many radially symmetric classical solutions. The main difficulties rely on the competition between the two nonlocal terms and on the presence of logarithmic kernels, which have not a prescribed sign. In addition, in order to find finite energy solutions, a suitable functional setting analysis is required.
Schrödinger equation in dimension two with competing logarithmic self-interaction
Azzollini, Antonio;
2025-01-01
Abstract
In this paper we study the equation (Formula presented.) where 8/3<4. By means of variational arguments, we find infinitely many radially symmetric classical solutions. The main difficulties rely on the competition between the two nonlocal terms and on the presence of logarithmic kernels, which have not a prescribed sign. In addition, in order to find finite energy solutions, a suitable functional setting analysis is required.File in questo prodotto:
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