Global structure of positive and sign-changing periodic solutions for the equations with Minkowski-curvature operator (Q6547813)

The authors investigate and show in the flat Minkowski space \N\[\N\mathbb L^{N+1}=\{(x,t): x\in \mathbb R^N, t\in \mathbb R\}\N\]\Nendowed with the Lorentzian metric, the existence of unbounded connected components of \(2\pi\)-periodic positive solutions for the equation with one-dimensional Minkowski-curvature operator\N\[\N-\left(\dfrac{u'}{\sqrt{1-u'^2}}\right)=\lambda a(x)f(u,u'), \quad x\in \mathbb R,\N\]\Nwhere \(\lambda\) is a positive parameter, \(a\in C(\mathbb R, \mathbb R)\) is a \(2\pi\)-periodic function and \(f\in C(\mathbb R \times \mathbb R, \mathbb R)\).