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; D'Avenia, Pietro; Pomponio, Alessio. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 64:4(2025). [10.1007/s00526-025-02989-5]
Schrödinger equation in dimension two with competing logarithmic self-interaction
d'Avenia, Pietro;Alessio, Pomponio
2025
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 | Dimensione | Formato | |
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