Existence of infinitely many radial nodal solutions for a Dirichlet problem involving mean curvature operator in Minkowski space - Xu Man (Electronic journal of qualitative theory of differential equations, 2020)
In this paper, we show the existence of infinitely many radial nodal solutions for the following Dirichlet problem involving mean curvature operator in Minkowski space −div ∇y 1−|∇y| 2 = λh(y) + g(|x|, y) in B, y = 0 on ∂B, where B = {x ∈ RN : |x| < 1} is the unit ball in RN, N ≥ 1, λ ≥ 0 is a parameter, h ∈ C(R) and g ∈ C(R+ × R). By bifurcation and topological methods, we prove the problem possesses infinitely many component of radial solutions branching off at λ = 0 from the trivial solution, each component being characterized by nodal properties.