THREE POSITIVE PERIODIC SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS

摘要

We establish the existence of at least three positive periodic solutions to the second order differential equation with periodic coefficients -(p(t)x'(t))' + q(t)x(t) = f(t, x(t)), t ∈ Rwhere f is continuous with f(t + T, x) = f(t,x) for (t,x) ∈ R × R and T > 0, p, q are continuous and T-periodic with p > 0 and q ≥ 0. We accomplish this by making growth assumptions on f, which can apply to many more cases than those discussed in recent works. An example to illustrate the main result is given.