Fredholm-Volterra integral equations with hypergeometric kernel (Q2771170)

The authors construct series solutions in \(L^2(-1,1)\times C(0,T)\) for the linear Fredholm-Volterra integral equation NEWLINE\[NEWLINE\lambda\phi(x, t)+\theta \int^1_{-1} K(x, s)\phi(s,t)\,ds+ \theta \int^t_0 F(\tau)\phi(x, \tau)\,d\tau= \gamma(t)+ \beta(t)x- f(x),NEWLINE\]NEWLINE on \(| x|\leq 1\), \(0\leq t\leq T\), under certain assumptions on the given functions \(F\), \(\gamma\), \(\beta\), \(f\), the kernel \(K\) and the constants \(\lambda\), \(\theta\). The problem occurs in elasticity theory and in hydrodynamics.