Multiple Solutions Of Biharmonic Equations Involving Singual Term

In this paper,we are concerned with the existence of the following two bihar-monic equations involving singular term.Fristly,we discuss the corresponding eigenvalue problem for the above two equations under some assumptions on g(x),and obtain the existence of the frist eigenvalue and its corresponding eigenfunction, on the basis of the above results,we consider equation (1) and (2) respectively:Equation (1):under giving some constrains to g(x),k(x),h(x),q,α, we discuss the existence of the solution in this case that s may be supercritical exponent and A is no larger thanλ₁: in the case ofλ<λ₁,applying the variational method and the theory of genus,we show the existence of infinite solutions;for the case ofλ=λ₁,we obtain the existence of solution by virtue of a new method:fibering method.Equation (2):taking s equal to 2^* =2N/(N-4) and taking corresponding changes to g(x), k(x),q,α,under the case that the following equation has no the expression of the acquired function,applying the acquired function for the imbedding mapping: we still get the existence of solution via variational method.