Existence of periodic solution for fourth-order generalized neutral p-Laplacian differential equation with attractive and repulsive singularities

Abstract

In this paper, we investigate the existence of a positive periodic solution for the following fourth-order p-Laplacian generalized neutral differential equation with attractive and repulsive singularities: where g has a singularity at the origin. The novelty of the present article is that we show that attractive and repulsive singularities enable the achievement of a new existence criterion of a positive periodic solution through an application of coincidence degree theory. Recent results in the literature are generalized and significantly improved.

Solutions for Some Specific Mathematical Physics Problems Issued from Modeling Real Phenomena: Part 2

“…Global weak solutions for evolution problems with logarithmic nonlinearities involving the p-pseudo-Laplacian are presented in [7][8][9][10], and those with p-Laplacian are studied in [11]. The existence of periodic solution [12], radial symmetry [13], symmetry [14], or principal eigenvalues [15] for fractional p-Laplacian, minimizers [16], and Picone type identities for p-Laplacian [17] or p-pseudo-Laplacian [18], regularity, and multiplicity results [19] represent interesting and topical issues that have important implications.…”