Study of Solutions for a quasilinear Elliptic Problem With negative exponents

2013/09/03 by Bin Guo, Guo, Bin, Wenjie Gao +3
Computer Science · Mathematics · #35J60 #35J70 #35K55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1309.0663

openalex publication_date 2013/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The authors of this paper deal with the existence and regularities of weak solutions to the homogenous \hboxDirichlet boundary value problem for the equation -\hboxdiv(|∇ u|^p-2∇ u)+|u|^p-2u=(f(x))/(u^α). The authors apply the method of regularization and \hboxLeray-Schauder fixed point theorem as well as a necessary compactness argument to prove the existence of solutions and then obtain some maximum norm estimates by constructing three suitable iterative sequences. Furthermore, we find that the critical exponent of m in ‖f‖_L^m(Ω). That is, when m lies in different intervals, the solutions of the problem mentioned belongs to different \hboxSobolev spaces. Besides, we prove that the solution of this problem is not in W^1,p₀(Ω) when α>2, while the solution of this problem is in W^1,p₀(Ω) when 1

Citations

• On a singular nonlinear elliptic boundary-value problem

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