We extend a recent result of Ricceri concerning the existence of three critical points of certain non-smooth functionals. Two applications are given, both in the theory of differential inclusions; the first one concerns a non-homogeneous Neumann boundary value problem, the second one treats a quasilinear elliptic inclusion problem in the whole RN .

We consider the numerical solution of quasilinear elliptic Neumann problems. The basic difficulty is the non-injectivity of the operator, which can be overcome by suitable factorization. We extend the gradient-finite element method (GFEM), introduced earlier by the authors for Dirichlet problems, to the Neumann problem. The algorithm is constructed and its convergence is proved.

Let {X1, . . . , Xm} be a basis of the space of horizontal vector fields on the Carnot group G = (R , ◦)(m < N). We establish regularity results for solutions to the following quasilinear degenerate elliptic obstacle problem ∫ Ω 〈〈AXu,Xu〉 p−2 2 AXu,X(v − u)〉dx ≥ ∫ Ω B(x, u,Xu)(v − u)dx

This paper deals with the quasilinear parabolic–elliptic chemotaxis system logistic source and nonlinear production, { u t = ∇ ⋅ ( D ) − S v + λ μ κ , x ∈ Ω > 0 Δ M f ‾ where 1 : | ∫ d are functions generalizing prototypes m α ℓ R . In case Fuest (2021) [5] obtained conditions for such that solutions blow up in finite time. However, above boundedness finite-time blow-up of have been not yet est...

We prove comparison results between viscosity sub and supersolutions of degenerate elliptic and parabolic equations associated to, possibly non-linear, Neumann boundary conditions. These results are obtained under more general assumptions on the equation (in particular the dependence in the gradient of the solution) and they allow applications to quasilinear, possibly singular, elliptic or para...

In this paper, an hp-local discontinuous Galerkin method is applied to a class of quasilinear elliptic boundary value problems which are of nonmonotone type. On hp-quasiuniform meshes, using the Brouwer fixed point theorem, it is shown that the discrete problem has a solution, and then using Lipschitz continuity of the discrete solution map, uniqueness is also proved. A priori error estimates i...