| In this thesis,we are concerned with the following Neumann boundary problem where Ω(?)RN is a bounded domain with smooth boundary and n denotes the outward normal vector on(?)Ω and λ are positive constants and γ∈ R\{0},and K(x)is a positive function in C2(Ω)∩ C1(Ω).Without loss of generality,we set c=1.Then we will prove the following two conclusions.When γ<0 and N≥ 1,the system has a unique solution.Particularly,the solution is a constant if and only if K(x)is a constant.When γ>0 and N=2,there is a mountain-pass solution if λ is sufficient small,and there are either boundary(or interior)peak solutions asλ→0. |
