摘要
In this paper,we consider the following problem {-Δu（x）＋u（x）=λ（u^p（x）＋h（x））,x∈R^N,u（x）∈h^1（R^N）,u（x）〉0,x∈R^N,（＊）where λ 〉 0 is a parameter,p =（N＋2）/（N—2）.We will prove that there exists a positive constant 0 〈 A＊ 〈 ＋00such that（＊） has a minimal positive solution for λ∈（0,λ＊）,no solution for λ 〉 λ＊,a unique solution for λ = λ＊.Furthermore,（＊） possesses at least two positive solutions when λ∈（0,λ＊） and 3 ≤ N ≤ 5.For N ≥ 6,under some monotonicity conditions of h we show that there exists a constant 0 〈λ＊＊ 〈 λ＊ such that problem（＊）possesses a unique solution for λ∈（0,λ＊＊）.
In this paper,we consider the following problem {-Δu（x）＋u（x）=λ（u^p（x）＋h（x））,x∈R^N,u（x）∈h^1（R^N）,u（x）〉0,x∈R^N,（＊）where λ 〉 0 is a parameter,p =（N＋2）/（N—2）.We will prove that there exists a positive constant 0 〈 A＊ 〈 ＋00such that（＊） has a minimal positive solution for λ∈（0,λ＊）,no solution for λ 〉 λ＊,a unique solution for λ = λ＊.Furthermore,（＊） possesses at least two positive solutions when λ∈（0,λ＊） and 3 ≤ N ≤ 5.For N ≥ 6,under some monotonicity conditions of h we show that there exists a constant 0 〈λ＊＊ 〈 λ＊ such that problem（＊）possesses a unique solution for λ∈（0,λ＊＊）.
基金
supported by the National Natural Science Foundation of China(No.11201132)
Scientific Research Foundation for Ph.D of Hubei University of Technology(No.BSQD12065)
supported by the Science Research Project of Hubei Provincial Department of education(No.d200614001)
