Existence Of Nontrivial Solutions For Semilinear Biharmonic Equation With Concave-convex Nonlinearities Involving Sign-changing Weight Funtions

In this master paper,we study existence of nontrivial solutions for semilinear biharmonic equation with concave-convex nonlinearities involving sign-changing weight functions:?(?)RN(N>4)is bounded smooth domains,00,we prove that the equation has at least one nontrivial solution for ??0(resp.??0)if f(x)+=0(resp.(-f)+=0);the equation has at least two nontrivial solutions if ????,f:={??R?(?f)+|q*?(0,?)}.