Electrostatic oscillations in cold inhomogeneous plasmas with compact support

Small-amplitude electrostatic oscillations in a cold plasma with compact support have been investigated. The same problem which was previously treated by Barston (1964) and Sedlacek (1971) was considered. A well behaved solution is constructed for sufficiently smooth initial conditions using a regular perturbation technique applied directly to Sedlacek's integro-differential equation. The method of solution presented here does not require inversion problems of rather complicated Fourier and Laplace transforms which are employed by the above authors.