Multiple solutions to some degenerate quasilinear equation with variable exponents via perturbation method (Q1682125)

This paper is concerned with the existence of signed and nodal solutions for a class of stationary PDEs driven by a nonhomogeneous differential operator with variable exponent. The main features of this paper are the lack of compactness (due to the study on the whole Euclidean space) and the presence of a gradient term with variable exponent. The basic arguments in the proof of the main existence result of this paper is the perturbation method combined with properties of invariant sets of the descending flow.