Oscillation properties of solutions to a nonselfadjoint spectral problem with spectral parameter in the boundary condition (Q2703931)

The author studies the following spectral problem NEWLINE\[NEWLINE-u''(x)+q(x)u(x)= \lambda u(x), \quad x\in (0,1),\qquad u(0)=0, \quad (a-\lambda)u'(1)+\lambda b u(1)=0,\tag{1}NEWLINE\]NEWLINE where \(a\) and \(b\) are positive numbers and \(q(x)\) is a continuous nonnegative function on the interval \([0,1]\). The oscillatory properties of eigenfunctions are discussed. Conditions are also presented under which a system of eigenfunctions to problem (1) forms a Riesz basis in the space \(L_2(0,1)\).