| 12 | Multiplicity and Uniqueness of Positive Solutions for Nonhomogeneous Semilinear Elliptic Equation with Critical Exponent显示文摘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**). | Na BA Yan-yan WANG Lie ZHENG | 2016 | Acta Mathematicae Applicatae Sinica2016，32，1： | 0 |
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