Weak solutions for the p-Laplacian with a nonlinear boundary condition at resonance
Rossi, Julio D.
Southwest Texas State University, Department of Mathematics
We study the existence of weak solutions to the equation Δpu = |u|p-2u + ƒ(x, u) with the nonlinear boundary condition |∇u|p-2 ∂u/ ∂v = λ|u|p-2 u-h(x, u). We assume Landesman-Lazer type conditions and use variational arguments to prove the existence of solutions.
p-Laplacian, Nonlinear boundary conditions, Resonance
Martinez, S., & Rossi, J. D. (2003). Weak solutions for the p-Laplacian with a nonlinear boundary condition at resonance. <i>Electronic Journal of Differential Equations, 2003</i>(27), pp. 1-14.