Some existence results for a new class of elliptic Kirchhoff equation with logarithmic source terms

Article type: Research Article

Authors: Boulaaras, Salah^{a; b; *; 1}

Affiliations: [a] Department of Mathematics, College of Sciences and Arts, Al-Rass, Qassim University, Kingdom of Saudi Arabia | [b] Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed Benbella. Algeria

Correspondence: [*] Corresponding author. Salah Boulaaras. E-mails: saleh_boulaares@yahoo.fr or S.Boularas@qu.edu.sa

Note: [1] This presented work is in memory of author’s father (1910–1999) Mr. Mahmoud ben Mouha Boulaaras.

Abstract:  In this paper, some new existence results of elliptic equation of Kirchhoff-type with changing sign data and logarithmic source terms are proved, by using three different methods: direct variational method, Galerkin approach and sub-super solutions method. Our study is natural extensions from the previous recent works in [2–19, 24, 38], where the authors have already studied the existence of positive solutions for some classes of Laplacian elliptic problems by using one classical method for a certain class of elliptic equations.

Keywords: Kirchhoff, existence, sub-supersolution, galerkin approach, elliptic equation

DOI: 10.3233/JIFS-190885

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 6, pp. 8335-8344, 2019