Weak solutions for the p-Laplacian with a nonlinear boundary condition at resonance - Martínez, S. (2003)
We study the existence of weak solutions to the equation Δpu = |u|p-2u + f(x, u) with the nonlinear boundary condition |∇u|p-2∂u/∂v = λ|u|p-2u - h(x, u). We assume Landesman-Lazer type conditions and use variational arguments to prove the existence of solutions.