Boundary value problems for differential inclusions with \(\varphi\)-Laplacian (Q2155919)

In this paper, the authors establish existence results for a second-order nonlinear differential inclusion problem \[ (\Phi(x'(t)))'\in F(t,x(t)) \text{ for a.e. } t\in [0,T], \] satisfying periodic or Dirichlet boundary conditions. The approach is based on the method of upper and lower solutions and on the topological degree technique. The involved multifunction \(F:[0,T]\times \mathbb{R}\to 2^{\mathbb{R}}\) is supposed to be compact, lower semi-continuous and with nonconvex values.