Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 27, pp. 1-14.
Title: Weak solutions for the p-Laplacian with a nonlinear boundary
condition at resonance
Authors: Sandra Martinez (Univ. Buenos Aires, Argentina)
Julio D. Rossi (Univ. Buenos Aires, Argentina)
Abstract:
We study the existence of weak solutions to the equation
$$ \Delta_p u = |u|^{p-2} u+f(x,u) $$
with the nonlinear boundary condition
$$
|\nabla u|^{p-2} \frac{\partial u}{\partial\nu}
= \lambda |u|^{p-2} u -h(x,u)\,.
$$
We assume Landesman-Lazer type conditions and use
variational arguments to prove the existence of solutions.
Submitted January 15, 2003. Published March 13, 2003.
Math Subject Classifications: 35P05, 35J60, 35J55.
Key Words: p-Laplacian; nonlinear boundary conditions; resonance.