Regularity Of Extremal Solution And Uniqueness Results For Second-order Nonlinear Eigenvalue Problems

We consider the following nonlinear eigenvalue problemswhere p>0, λ≥0, Ω(?)Rn is smooth bounded domain and f∈C(ˉΩ) is a nonnegativefunction. Our study is motivated by a simple Micro-Electromechanical Systems (MEMS)device model. We fnd some new phenomena about the regularity results by the clas-sifcation of entire solutions. Besides, we also consider the uniqueness of solutions byRellich-Pohozaev type estimates.This thesis consists of four chaptersChapter1states the origin of our problems, history of study and the new resultsabout the regularity and uniqueness. Besides, we,in this chapter, give some notions andsymbols. In chapter2we will study the regularity of the extremal solution for the casesof the ball and generally domains. In chapter3the uniqueness results will be given byRellich-Pohozaev type estimates. In fnally we devote to the classifcation of the entiresolutions.