Ground state sign-changing solutions for Kirchhoff equations with logarithmic nonlinearity

Wen, Lixi and Xianhua, Tang and Chen, Sitong: Ground state sign-changing solutions for Kirchhoff equations with logarithmic nonlinearity.

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Abstract

In this paper, we study Kirchhoff equations with logarithmic nonlinearity: −(a + b R |∇u| 2 )∆u + V(x)u = |u| p−2u ln u 2 , in Ω, u = 0, on ∂Ω, where a, b > 0 are constants, 4 < p < 2 , Ω is a smooth bounded domain of R3 and V : Ω → R. Using constraint variational method, topological degree theory and some new energy estimate inequalities, we prove the existence of ground state solutions and ground state sign-changing solutions with precisely two nodal domains. In particular, some new tricks are used to overcome the difficulties that |u| p−2u ln u 2 is sign-changing and satisfies neither the monotonicity condition nor the Ambrosetti–Rabinowitz condition.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 47
ISSN: 1417-3875
Page Range: pp. 1-13
DOI: https://doi.org/10.14232/ejqtde.2019.1.47
Uncontrolled Keywords: Kirchhoff, Differenciálegyenlet, Logaritmus
Additional Information: Bibliogr.: p. 11-13. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 30. 07:55
Last Modified: 2020. Jul. 29. 12:24
URI: http://acta.bibl.u-szeged.hu/id/eprint/62271

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