부산대학교 도서관

We consider the wave equation in three space dimensions perturbed by a time-periodic potential with compact support in space, multiplied by a small parameter, ε. When ε = 0, the scattering theory of Lax and Phillips defines scattering frequencies which describe the decay of solutions in the neighborhood of the support of the potential. For ε > 0, scattering frequencies are defined; they are analogous to Floquet exponents. We show that when the frequency of the time-periodic potential is a multiple of the real part of a scattering frequency σ 0 for the time-independent case, resonance occurs. When e increases from zero, the scattering frequency σ 0 splits in a symmetric fashion, defining outgoing solutions which decay faster or slower than those of the time-independent problem. An example is given in the case of spherical symmetry of the potential. [ABSTRACT FROM AUTHOR]