Abstract
In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a gravitational force acting on the body of the fluid. We prove the existence of global continua of classical solutions that are periodic and traveling. This is accomplished by globally continuing the curves of small-amplitude solutions obtained by the author in [25]. We do this in two ways: first, by means of a degree theoretic theorem in the spirit of Rabinowitz, and second via the analytic continuation method of Dancer.
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