Bifurcation for a Class of Fourth-Order Stationary Kuramoto-Sivashinsky Equations Under Navier Boundary Condition

Abstract

In this paper, we study the bifurcation of semilinear elliptic problem of fourth-order with Navier boundary conditions. We discuss the existence and the uniqueness of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of problems of bifurcation for a class of elliptic problems we also establish the asymptotic behavior of the solution around the bifurcation point.