Nonlinear noncoercive Neumann problems

Noncoercive convection-diffusion elliptic problems with Neumann boundary conditions

We study the existence and uniqueness of solutions of the convective-diffusive elliptic equation −div(D∇u) + div(V u) = f posed in a bounded domain Ω ⊂ RN , with pure Neumann boundary conditions D∇u · n = (V · n)u on ∂Ω. Under the assumption that V ∈ Lp(Ω)N with p = N if N ≥ 3 (resp. p > 2 if N = 2), we prove that the problem has a solution u ∈ H1(Ω) if ∫ Ω f dx = 0, and also that the kernel is...

Qualitative properties of some noncoercive functionals arising from nonlinear boundary value problems

Gradient-finite Element Method for Nonlinear Neumann Problems

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.

Generalized BSDEs and nonlinear Neumann boundary value problems

We study a new class of backward stochastic di€erential equations, which involves the integral with respect to a continuous increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial di€erential equations with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic equations.

On Noncoercive Elliptic Problems with Discontinuities

In this paper using the critical point theory of Chang [4] for locally Lipschitz functionals we prove an existence theorem for noncoercive Neumann problems with discontinuous nonlinearities. We use the mountain-pass theorem to obtain a nontrivial solution.