On the mixed boundary-value problem in the halfstrip for the elliptic equation (Q1333653)

The aim of this article is to prove the existence theorem for the following problem: find a function \(g(w)\) which is continuous in the halfstrip \(D=\{w\): \(| \text{Re } w|< 1/2\), \(\text{Im } w<0\}\) with locally integrable generalized derivatives, and is continuously extendible to the finite points of \(\partial D\), \(| g(w)- \pi i w|= o(| w|)\) with \(w\to\infty\), if \[ g^ \prime_{\overline {w}}= \lambda (w) g^ \prime_ w +h(w), \qquad w\in D, \] \[ \text{Re } g(w)|_{w= u\in (-1/2, 1/2)}= \Omega (u); \qquad \text{Im } g(w)|_{w=\pm 1/2+iv, v\in (-\infty, 0)}= \pm \pi/2. \]