Nontrivial Fučík spectrum of one non-selfadjoint operator
The Fučík spectrum of the boundary value problem \[ u''(x)=\begin{cases} \alpha u^+(x)-\beta u^-(x), & x\in (0,\pi)\\ u'(0) =u'(\xi),\;u(\pi)=u(\eta), & \xi\in (0,\pi),\;\eta \in (0,\pi) \end{cases} \] is the set of all pairs \((\alpha,\beta )\) of real numbers for which this problem has a nontrivial solution. The left-hand side of this problem is a linear but non-selfadjoint operator, however with only real spectrum. The author gives explicit formulas for the Fučík spectrum as well as a number of pictures with different parts of this spectrum. It is explained and discussed how this behaviour differs from that of the Fučík spectrum of the Sturm-Liouville operator with self-adjoint boundary conditions.
scientific article; zbMATH DE number 5355039