Global bifurcation result for Dirichlet and Neumann p-biharmonic problem

Abstract.

We consider the Dirichlet and Neumann fourth-order quasilinear boundary value problem for

$$(|u^{\prime\prime}|^{p-2}u^{\prime\prime})^{\prime\prime}=\lambda|u|^{p-2}u+g(t,\lambda,u,u^{\prime},u^{\prime\prime})\quad \hbox{in} \quad [0, 1].$$

We determine the Leray–Schauder degree of the associated operators. As a standard consequence, we then prove a global bifurcation result and existence of the solution in nonresonance.