MULTIPLE BOUNDED VARIATION SOLUTIONS OF A PERIODICALLY PERTURBED SINE-CURVATURE EQUATION

Abstract

We prove the existence of at least two T-periodic solutions, not differing from each other by an integer multiple of 2π, of the sine-curvature equation [Formula: see text] We assume that A ∈ ℝ and [Formula: see text] is a T-periodic function such that [Formula: see text] and, e.g. ‖h‖ L ∞ < 4/T. Our approach is variational and makes use of basic results of non-smooth critical point theory in the space of bounded variation functions.