Título:	Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains
Autor(es):	Tong, Yonghui Guo, Hui Figueiredo, Giovany de Jesus Malcher
E-mail do autor:	mailto:myyhtong@163.com mailto:huiguo_math@163.com mailto:giovany_ufpa@yahoo.com.br
Assunto:	Schrödinger, Equação de Equações diferenciais
Data de publicação:	2021
Editora:	University of Szeged
Referência:	TONG, Yonghui; GUO, Hui; FIGUEIREDO, Giovany M. Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains. Electronic Journal of Qualitative Theory of Differential Equations, n. 70, 1–14, 2021. DOI 10.14232/ejqtde.2021.1.70. Disponível em: http://www.math.u-szeged.hu/ejqtde/p9311.pdf. Acesso em: 05 out. 2022.
Abstract:	We consider a class of fractional logarithmic Schrödinger equation in bounded domains. First, by means of the constraint variational method, quantitative deformation lemma and some new inequalities, the positive ground state solutions and ground state sign-changing solutions are obtained. These inequalities are derived from the special properties of fractional logarithmic equations and are critical for us to obtain our main results. Moreover, we show that the energy of any sign-changing solution is strictly larger than twice the ground state energy. Finally, we obtain that the equation has infinitely many nontrivial solutions. Our result complements the existing ones to fractional Schrödinger problems when the nonlinearity is sign-changing and satisfies neither the monotonicity condition nor Ambrosetti–Rabinowitz condition.
Licença:	Electronic Journal of Qualitative Theory of Differential Equations - EJQTDE applies the Creative Commons Attribution (CC BY) license to articles and other works we publish. It is to be understood that once a paper is published, it cannot be removed or corrected, although a correction can be published later in the journal and a notation made in the original article telling where a correction appears. Fonte: http://www.math.u-szeged.hu/ejqtde/submit.html. Acesso em: 05 out. 2022.
DOI:	https://doi.org/10.14232/ejqtde.2021.1.70
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