On Global Solution for a Class of p(x)-Laplacian Equations with Logarithmic Nonlinearity

In this paper, we consider a class of p ( x )-Laplacian equations with logarithmic source terms. Using the potential well method combined with the Nehari manifold, we prove some results on the global existence and blow-up of weak solutions in the subcritical case. Moreover, we also obtain decay esti...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 21; no. 2
Main Authors Van Chuong, Quach, Nhan, Le Cong, Truong, Le Xuan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2024
Springer Nature B.V
Subjects
Laplace equation
Logarithms
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Upper bounds
global existence
blow-up
35A01
35B44
(
variable exponent
Nehari manifold
35K55
Laplacian operator
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Summary:In this paper, we consider a class of p ( x )-Laplacian equations with logarithmic source terms. Using the potential well method combined with the Nehari manifold, we prove some results on the global existence and blow-up of weak solutions in the subcritical case. Moreover, we also obtain decay estimates for the global weak solutions. Otherwise, we give an upper bound for the maximal existence time of the blow-up weak solutions under different levels of initial energy. The main difficulties here not only come from the usual difficulties in variable exponent spaces but also from the sign-changing property of the logarithmic function. Our results improve (Boudjeriou in J Elliptic Parabol Equ 6:773–794 2020) and fill the gaps in Liu et al. (Nonlinear Anal Real World Appl 64:103449, 2022). Notice that the methods here are different from Boudjeriou (2020) and can be used to extend (Zeng et al. in J Nonlinear Math Phys 29:41–57, 2022).
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-024-02604-5