Kim, Yun-Ho A global bifurcation for nonlinear elliptic equations involving nonhomogeneous operators of \(p(x)\)-Laplace type. (English) Zbl 1413.35061 Adv. Stud. Contemp. Math., Kyungshang 28, No. 1, 27-39 (2018). Summary: We are concerned with the following nonlinear problem (Equation presented) subject to Dirichlet boundary condition, provided that \(\mu\) is not an eigenvalue of the \(p(x)\)-Laplacian. The aim of this paper is to study the structure of the set of weak solutions of nonlinear equations of \(p(x)\)-Laplace type, by applying a bifurcation result for nonlinear operator equations. MSC: 35B32 Bifurcations in context of PDEs 35D30 Weak solutions to PDEs 35J60 Nonlinear elliptic equations 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems Keywords:differential-difference equation; integro-differential-difference equation; Laplace transform; Adomian polynomials; Laplace decomposition method and homotopy analysis method PDFBibTeX XMLCite \textit{Y.-H. Kim}, Adv. Stud. Contemp. Math., Kyungshang 28, No. 1, 27--39 (2018; Zbl 1413.35061)