Abstract
For p∈R and p>1 we consider the second-order ordinary differential equation u″−u+up=0, which has a one-parameter family of periodic solutions satisfying (u(0),u′(0))=(u1,0) with u1∈(0,1). We prove that the so-called period function T(u1), which represents the period of the periodic solution, is strictly decreasing on (0,1). This result is also applied to completely determine the global bifurcation diagram of interior single-peak solutions in the Neumann boundary value problem of u″+λ(−u+up)=0 in (−1,1) with u′(±1)=0, where λ is a control parameter.
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