Spectral symmetry of solutions of boundary value problems in Banach algebras
Tom 128 / 2022
Annales Polonici Mathematici 128 (2022), 39-48
MSC: Primary 34B15; Secondary 34C14, 46H99.
DOI: 10.4064/ap210520-4-10
Opublikowany online: 20 January 2022
Streszczenie
For Banach algebras and solutions u:[0,1] \to {\cal A} of u”(t)+f(u(t))+ \lambda u’(t)^2=0, u(0)=0, u(1)=0, we prove symmetry of the spectrum \sigma (u(t)), that is, \sigma (u(t)) = \sigma (u(1-t)) for all t \in [0,1], whenever \sigma (u([0,1])) lies in a cone of the complex plane.
