In this paper, the following Fuchsian equation with four singularities is studied:
with , , and the parameters , , , , satisfy the Fuchs identity and the additional conditions , , , . The other parameter is a small positive one.
A boundary problem on the interval is posed for equation (1) with the boundary conditions , . The eigenvalues of this problem are functions of the parameter .
The authors study the behaviour of the eigenvalue curves in the vicinity of , i.e. for . The qualitative behaviour of the eigenfunctions is also studied.
A nice application of the obtained results is demonstrated on an important physical model – the plastic deformation of crystalline materials under stress.