Eigenvalues of an Inhomogeneous Elliptic Equation Involving the p(x)-Laplacian Operator and Logarithmic Nonlinearity, Part I

The main aim of this paper is to examine the eigenvalues of doubly inhomogeneous elliptic equations involving thep(x)-Laplacian operator and logarithmic nonlinearity. We employ Ekeland’s variational principle via sublinearity to analyse the spectrum structure and obtain results concerning multiplicity by establishing sufficient conditions. Our results extend those of a recent paper that appears in the literature. 2020 Mathematics Subject Classification. 35J62; 35P30. Key words and phrases. inhomogeneous elliptic equations;p(x)-Laplacian operator; logarithmic nonlin- earity; Ekeland’s variational principle; variable exponents.