Non-Existence Of Nonlinear Biharmonic Equation With Negative Exponents

The main objective of this article is to study positive solutions of biharmonic equation which is a generalized version of Q-curvature equation,△2u+Qu-q=0in R3, with q>0, Q being a known function on R3.The structure of the dissertation is as follows:In chapter one, we introduce the backgrounds and origins of the equation that has been investigated, then review some revelent research results and present the main results of this article.In chapter two, firstly, we recalled the history of Pohozaev’s identity, which plays an important role in the research of PDE. Then, considered the differences between second order equations and hider order equations, we can derive the general identity we wanted.In chapter three, first, we establish a priori estimate for the solutions of differential equation. Next, we prove the equivalence of the differential equation and the integral equation so as to use the integral equation to discuss the properties of solutions. Combined with the two aspects of the income, thus get the expected conclusion.In chapter four, we analyze the equation by using another method-the shooting method.