Boundary Value Problems For A Semilinear Elliptic Equation With Singular Nonlinearity

This paper proposes structure of solution of boundary value problems for a semilinear elliptic equation with singular nonlinearity. It is seen that the structure of solutions relies on the boundary values. The global branches of solutions of the boundary value problems are established. Moreover, some Liouville type results for the entire solutions of the equation are also obtained.We intend to separate the dissertation into five chapters as following:In Chapter one, we first present the applications practical and related work of these boundary value problems. Then, the main work of this paper is briefly introduced.In Chapter two, firstly, we recall the definitions of the subsolution and supersolution of Poisson equation and the maximum principle. secondly, we introduce the inequality of Sobolev space. In the end, we obtain the existence and uniqueness results for the problem ?P_?? with f satisfies ?F₁?.In Chapter three, we first recall the conception about the Schcuder interior estimate. Then we obtain the global branches of solutions of ?P_?? with f satisfies ?F₁?.In Chapter four, we obtain some Liouville type results in RN, and thus prove these results.In Chapter five, we obtain the global branches of solutions of ?P_?? and ?P_?^?? with f satisfies ?F₂? and some Liouville type results.