Multivalued \(p\)-Liénard systems (Q2388412)

The authors study the following multi-valued \(p\)-Liénard system driven by the vector p-Laplacian differential operator with Dirichlet conditions of the type \[ (\| x'(t) \|^{p-2}x'(t))' + \frac{d}{dt} \nabla G(x(t)) + F(t, x(t), x'(t)) \ni 0 \text{ a.e. on } T=[0,b], \] \[ x(0)=x(b)=0, \quad1<p<\infty, \] where \(F:T \times \mathbb R^N \times \mathbb R^N \to 2^{\mathbb R^N} \) is a multifunction with nonempty, compact and convex values and \(G \in C^2(\mathbb R^N ,\mathbb R)\). The authors prove the existence of solutions by assuming conditions of nonuniform nonresonance with respect to the first weighted eigenvalue of the negative vector ordinary \(p\)-Laplacian with Dirichlet boundary conditions and using a multi-valued version of the Leray-Schauder alternative principle.