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

We show the existence of unbounded connected components of 2π-periodic positive solutions for the equations with one-dimensional Minkowski-curvature operator − u ′ 1 − u ′ 2 ′ = λ a (x) f (u , u ′ ) , x ∈ R , where λ > 0 is a parameter, a ∈ C (R , R) is a 2π-periodic sign-changing function with ∫ 0 2 π a (x) d x < 0 , f ∈ C (R × R , R) satisfies a generalized regular-oscillation condition. Moreover, for the special case that f does not contain derivative term, we also investigate the global structure of 2π-periodic odd/even sign-changing solutions set under some parity conditions. The proof of our main results are based upon bifurcation techniques. [ABSTRACT FROM AUTHOR]