Contact problem for two strings with variable tensions

The model of a string with the variable continuous tension is proposed. This model is based on the limiting process for an $N$-tier string with different constant tensions. The one-side contact problem for two strings under the given loading is considered. The left end of each string is fixed and the right one is free. The problem is stated clearly, uniqueness of the solution is proved, and analytical solutions of the problem for some special cases are found. It is shown that the strings may contact both at one point and in the segment.