Multiplicity of Forced Oscillations for Scalar Differential Equations
Pera, Maria Patrizia
Southwest Texas State University, Department of Mathematics
We give, via topological methods, multiplicity results for small periodic perturbations of scalar second order differential equations. In particular, we show that the equation ẍ = g(x) + εf(t, x, ẋ), where g is C1 and ƒ is continuous and periodic in t, has n forced oscillations, provided that g changes sign n times (n > 1).
Forced oscillations, Ordinary differential equations, Multiplicity of periodic solutions
Furi, M., Pera, M. P., & Spadini, M. (2001). Multiplicity of forced oscillations for scalar differential equations. <i>Electronic Journal of Differential Equations, 2001</i>(36), pp. 1-9.