Computing the Location and the Direction of Bifurcation for Sign Changing Solutions
نویسندگان
چکیده
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) . If 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.
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تاریخ انتشار 2010