Computing the Location and the Direction of Bifurcation for Sign Changing Solutions
We consider sign-changing solutions of the Dirichlet problem u +λ f(u )= 0, 0 < x < 1, u(0 )= u(1 )= 0, with n 0 interior roots. We give a necessary and sufficient condition that a turn occurs at the solution (λ,u(x)), depending only on the maximum value of the solution u(x) .I f a turn does occur, we give another formula allowing to compute the direction of the turn. Our results generalize those in P. Korman, Y. Li and T. Ouyang (6), where positive solutions were considered. We give similar results for Neumann problem.
& Li, Y.
(2010). Computing the Location and the Direction of Bifurcation for Sign Changing Solutions. Differential Equations and Applications, 2 (1), 1-13.