On the resonance set in a fourth-order equation with jumping nonlinearity. (English) Zbl 1022.35011

Campos, Juan; Dancer, Edward Norman

Differ. Integral Equ. 14, No. 3, 257-272 (2001).

The authors give a geometric understanding of the Fučík spectrum of several fourth-order problems. This investigation was suggested by S. Fučík [Solvability of Nonlinear Equations and boundary value problems, Reidel, Dordrecht (1980; Zbl 0453.47035)], where it is asked to give a description of this set. The situation resembles the known cases of second-order equations, where analytic branches bifurcate from the eigenvalues in the diagonal.

Reviewer: Josef Diblík (Brno)

MSC:

35J40

Boundary value problems for higher-order elliptic equations

Keywords:

Fučík spectrum; fourth-order problem

Citations:

Zbl 0453.47035