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The biharmonic equation is a fourth-order partial differential equation. It is well-known that the weak solutions of the biharmonic elliptic equation with Sobolev critical exponent are the critical points of the corresponding energy functional. Under some conditions, by using the variational method, we study the mountain pass lemma and Palais-Smale theory to show the existence of nontrivial solutions for this equation in a bounded domain. Moreover, according to the properties of coefficient function f, we discuss the multiplicity of nontrivial solutions for this equation. |
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