Some Research On Solutions For Hénon Type Equations

In this thesis, we discuss the existence of nontrivial solution for critical and subcritical Henon equation. In the subcritical case, we study the existence of ground state solutions (least energy solutions) for a class of Henon type equation as well as asymptotic behavior of the solution as pâ†'2*. This thesis is divided into three chapters.In Chapter 1, we introduce the backgrounds of the problem and the main results of this thesis.Chapter 2 is concerned with the existence of nontrivial solution for whereΩ(?)Rn is bounded domain which satisfies the exterior sphere property. This chapter is divided into three sections according to the value of A.In Chapter 3, we investigate ground state solutions for the Henon type equation whereΩ=Bk(0,1)×Bn-k(0,1)(?)Rn and x= (y, z)∈E Rk×Rn-k. We study the existence of cylindrically symmetric and non-cylindrically symmetric ground state solutions of the problem. We also investigate asymptotic behavior of the ground state solution when p tends to the critical exponent 2*=2n/n-2 if n≥3.