Properties of the Fucik spectrum of p-laplacian with nonlinear boundary conditions

MARTÍNEZ, SANDRA RITA; ROSSI, JULIO D

CMM, Santiago de Chile, Chile

Congreso; Inverse Problems and Nonlinear Analysis; 2003

In this paper we prove that there exists a first curve of theFuv{c}ik spectrum of the problem $Delta_p u = |u|^{p-2} u$ in$o$ with a nonlinear boundary condition given by $| ablau|^{p-2}partial u/partial u = alpha (u^+)^{p-1}-eta (u^-)^{p-1} $on the boundary of the domain. We also prove that there exists asequence of curves of the Fuv{c}ik spectrum which exist locallyin the neighborhood of suitable eigenvalues of the $p$-laplacianwith a nonlinear boundary condition. Finally, we study a resonanceproblem with respect to the Fuv{c}ik spectrum.