Positive solutions for a fourth-order integral boundary value problem involving impulses and the p-Laplacian - Xu, Jiafa; Yang, Zhichun; O’Regan, Donal; Liao, Jiangdong (Nonlinear Analysis: Modelling and Control, 2026)
In this paper, we investigate the existence of positive solutions for a fourth-order integral boundary value problem involving impulses and the p-Laplacian operator. First, we construct a linear operator that incorporates impulsive effects, and then analyze its spectral radius properties. Subsequently, under suitable conditions on the spectral radius, we apply the fixed point index theory to establish existence theorems for the problem. Our results cover cases where the nonlinear term exhibits (p – 1)-superlinear/sublinear growth, and the impulsive term satisfies superlinear/sublinear growth conditions.
Keywords: fourth-order integral boundary value problem; positive solutions; fixed point index