Multiple Solutions For Biharmonic Equations With Concave-convex Nonlinearities

In this paper,we consider biharmonic equations involving concave-convex non-linearities and sign-changing weight function. We consider the following Dirichlet boundary value problem where Ω is a bounded smooth domain in RN with N>4,n is the unit exterior normal on aQ,入>0is a parmeter,a(x):Ω�'R is a continuous function which change sign in Ω,6(x)is a positive continuous function,and0<g<1<p<N-4/N+4.Define the functional It is well known that the solutions of(1.1)are the critical points of the energy functional Jλ·For1≤r≤∞we denote by|·|rthe Lr(Q)norm whereas,we denote by·‖the H02(Ω)norm,that is‖u‖2=∫|△u|2dx.Define the Nehari manifold as follow Mǐ={u∈H02(Ω)\{0}:...