Periodic solutions for indefinite singular perturbations of the relativistic acceleration

Abstract

Using the Leray–Schauder degree, we study the existence of solutions for the following periodic differential equation with relativistic acceleration and singular nonlinearity:where μ > 1 and the weight h: [0, T] → ℝ is a continuous sign-changing function. There are no a priori estimates on the set of positive solutions (a condition used in general to apply the Leray–Schauder degree), and we prove that no solution of the equation appears on the boundary of an unbounded open set during the deformation to an autonomous problem.