A degenerate bifurcation from simple eigenvalue theorem

&lt;abstract&gt;&lt;p&gt;A new bifurcation from simple eigenvalue theorem is proved for general nonlinear functional equations. It is shown that in this bifurcation scenario, the bifurcating solutions are on a curve which is tangent to the line of trivial solutions, while in typical bifurcations the curve of bifurcating solutions is transversal to the line of trivial ones. The stability of bifurcating solutions can be determined, and examples from partial differential equations are shown to demonstrate such bifurcations.&lt;/p&gt;&lt;/abstract&gt;</jats:p