2023/06/02 by Zhanbing Bai, Yizhe Feng, Bai, Zhanbing +1
Engineering · Mathematics · #03H10 #05J50 #35D30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2306.01319
openalex publication_date 2023/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study a class of double phase systems which contain the singular and mixed nonlinear terms. Unlike the single equation, the mixed nonlinear terms make the problem more complicate. The geometry of the fibering mapping has multiple possibilities. To overcome the difficulties posed by the mixed nonlinear terms, we need to repeatedly construct concave functions, discuss different cases, and use the properties of concave functions and basic inequalities such as Holder inequality, Poincares inequality and Youngs inequality. By the use of the Nehari manifold, the existence and multiplicity of positive solutions which have nonnegative energy are obtained. It is worth mentioning that we note the existence of saddle point solution(a station point that is not a local minimum), see Remark 3.1.