【摘 要】
：
Let B1 be the unit ball in RN with N ≥ 2.Let f ∈ C1([0,∞),R),f(0)= 0,f(β)= β,f(s)< s for s ∈(0,β),f(s)> s for s ∈(β,∞)and f′(β)> λrk.D.Bonheure
【出 处】
：
2016年上海微分方程与动力系统会议
论文部分内容阅读
Let B1 be the unit ball in RN with N ≥ 2.Let f ∈ C1([0,∞),R),f(0)= 0,f(β)= β,f(s)< s for s ∈(0,β),f(s)> s for s ∈(β,∞)and f′(β)> λrk.D.Bonheure,B.Noris and T.Weth [Ann.I.H.Poincar(e)-AN 29(2012)] proved the existence of nondecreasing,radial positive solutions of the semilinear Neumann problem -Δu+u = f(u)in B1 (e)υu = 0 on (e)B1 for k = 2,and they conjectured that there exists a radial solution with k intersections with β provided that f′(β)> λrk for k > 2,where λrk is the k-th radial eigenvalue of Δ+1 in the unit ball with Neumann boundary conditions.
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