Electron. J. Diff. Eqns., Vol. 2003(2003), No. 27, pp. 1-14.

Weak solutions for the p-Laplacian with a nonlinear boundary condition at resonance

Sandra Martinez & Julio D. Rossi

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.

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  Sandra Martinez
Departamento de Matematica, FCEyN
UBA (1428) Buenos Aires, Argentina
email: smartin@dm.uba.ar
Julio D. Rossi
Departamento de Matematica, FCEyN
UBA (1428) Buenos Aires, Argentina
and
Facultad de Matematicas, Universidad Catolica
Casilla 306 Correo 22 Santiago, Chile
email: jrossi@dm.uba.ar, jrossi@mat.puc.cl

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